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Topol. 23(1), 169–178 (2022)\nAzam, A.: Fuzzy fixed points of fuzzy mappings via a rational inequality. Hacet. J. Math. Stat. 40(3), 421–431 (2011)\nAzam, A., Arshad, M., Beg, I.: Fixed points of fuzzy contractive and fuzzy locally contractive maps. Chaos Solitons Fractals 42(5), 2836–2841 (2009)\nAzam, A., Beg, I.: Common fixed points of fuzzy maps. Math. Comput. Model. 49(7–8), 1331–1336 (2009)\nBanach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundam. Math. 3(1), 133–181 (1922)\nButnariu, D.: Fixed point for fuzzy mapping. Fuzzy Sets Syst. 7(1), 199–207 (1982)\nEscardo, M.H.: PCF extended with real numbers. Theor. Comput. Sci. 162(1), 79–115 (1996)\nGoguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(1), 145–174 (1967)\nGulzar, M., Dilawar, F., Alghazzawi, D., Mateen, M.H.: A note on complex fuzzy subfield. Indones. J. Electr. Eng. Comput. Sci. 21(2), 1048–1056 (2021)\nHeilpern, S.: Fuzzy mappings and fixed point theorem. J. Math. Anal. Appl. 83(2), 566–569 (1981)\nKanwal, S., Ali, A., Al Mazrooei, A., Garcia, G.S.: Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces. AIMS Math. 8(5), 10095–10112 (2023)\nKanwal, S., Al Mazrooei, A., Garcia, G.S., Gulzar, M.: Some fixed point results for fuzzy generalizations of Nadler’s contraction in b-metric spaces. AIMS Math. 8(5), 10177–10195 (2023)\nKanwal, S., Azam, A.: Bounded lattice fuzzy coincidence theorems with applications. J. Intell. Fuzzy Syst. 36, 1–15 (2019). https:\u002F\u002Fdoi.org\u002F10.3233\u002FJIFS-181754\nKanwal, S., Shagari, M.S., Aydi, H., Mukheimer, A., Abdeljawad, T.: Common fixed-point results of fuzzy mappings and applications on stochastic Volterra integral equations. J. Inequal. Appl. 2022, 110 (2022). https:\u002F\u002Fdoi.org\u002F10.1186\u002Fs13660-022-02849-2\nKanwal, S., Hanif, U., Noorwali, M.E., Alam, M.A.: Existence of \\(\\alpha _{L}\\)-fuzzy fixed points of L-fuzzy mappings. Math. 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Intell. Fuzzy Syst. 36(4), 3413–3422 (2019)\nRasham, T., Saeed, F., Agarwal, R.P., Hussain, A., Felhi, A.: Symmetrical hybrid coupled fuzzy fixed-point results on closed ball in fuzzy metric space with applications. Symmetry 15(1), 30 (2023)\nSahin, H., Aslantas, M., Nasir Nasir, A.A.: Some extended results for multivalued F-contraction mappings. Axioms 12, 116 (2023). https:\u002F\u002Fdoi.org\u002F10.3390\u002Faxioms12020116\nShazad, A., Rasham, T., Marino, G., Shoaib, A.: On fixed point results for \\(\\alpha ^{\\ast}-\\psi \\)-dominated fuzzy contractive mappings with graph. J. Intell. Fuzzy Syst. 38(8), 3093–3103 (2020)\nZadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)\nZhan, J., Xu, W.: Two types of coverings based multigranulation rough fuzzy sets and applications to decision making. Artif. Intell. Rev. 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J. Glob. Optim. 19, 83–102 (2001)\nMatsui, T.: NP-hardness of linear multiplicative programming and related problems. J. Glob. Optim. 9, 113–119 (1996)\nJiao, H.W., Liu, S.Y.: A practicable branch and bound algorithm for sum of linear ratios problem. Eur. J. Oper. Res. 243, 723–730 (2015)\nWang, C., Shen, P.: A global optimization algorithm for linear fractional programming. Appl. Math. Comput. 204(1), 281–287 (2008)\nShen, P., Wang, C.: Global optimization for sum of linear ratios problem. Appl. Math. Comput. 176, 219–229 (2006)\nLim, S., Zhu, J.: Integrated data envelopment analysis: global vs. local optimum. Eur. J. Oper. Res. 229, 276–278 (2013)\nRao, M.R.: Cluster analysis and mathematical programming. J. Am. Stat. Assoc. 66, 622–626 (1971)\nDrezner, Z., Manes, R.P., Whinston, A.: Queueing-location problems on the plane. Nav. Res. Logist. 37, 929–935 (1990)\nBenson, H.: A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem. Eur. J. Oper. Res. 182, 597–611 (2007)\nCarlsson, J.G., Shi, J.: A linear relaxation algorithm for solving the sum-of-linear-ratios problem with lower dimension. Oper. Res. Lett. 41(4), 381–389 (2013)\nDepetrini, D., Locatelli, M.: Approximation of linear fractional-multiplicative problems. Math. Program. 128, 437–443 (2011)\nShen, P., Li, W., Liang, Y.: Branch-reduction-bound algorithm for linear sum-of-ratios fractional programs. Pac. J. Optim. 11(1), 79–99 (2015)\nKonno, H., Yajima, Y., Matsui, T.: Parametric simplex algorithms for solving a special class of nonconvex minimization problems. J. Glob. Optim. 1, 65–81 (1991)\nKonno, H., Yamashita, H.: Minimization of the sum and the product of several linear fractional functions. Nav. Res. Logist. 46, 583–596 (1999)\nMuu, L.D., Tam, B.T., Schaible, S.: Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions. J. Glob. Optim. 6, 179–191 (1995)\nJi, Y., Zhang, K., Qu, S.: A deterministic global optimization algorithm. Appl. Math. Comput. 185, 382–387 (2007)\nJiao, H., Liu, S.: A practicable branch and bound algorithm for sum of linear ratios problem. Eur. J. Oper. Res. 243, 723–730 (2015)\nJiao, H., Wang, Z., Chen, Y.: Global optimization algorithm for sum of generalized polynomial ratios problem. Appl. Math. Model. 37, 187–197 (2013)\nTuy, H.: Convex Analysis and Global Optimization. Kluwer, Dordrecht (1978)\nMajhi, J., Janardan, R., Schwerdt, J., Smid, M., Gupta, P.: Minimizing support structures and trapped area in two-dimensional layered manufacturing. Comput. Geom. Theory Appl. 12, 241–267 (1999)\nChen, D., Daescu, O., Hu, X., Wu, X., Xu, J.: Determining an optimal penetration among weighted regions in two and three dimensions. J. Comb. Optim. 5, 59–79 (2001)\nChen, D., Daescu, O., Dai, Y., Katoh, N., Wu, X., Xu, J.: Efficient algorithms and implementations for optimizing the sum of linear fractional functions, with applications. J. Comb. Optim. 9, 69–90 (2005)\nPei, Y., Zhu, D.: Global optimization method for maximizing the sum of difference of convex functions ratios over nonconvex region. J. Appl. Math. Comput. 41, 153–169 (2013)",{"EN":468},"This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.",{"EN":470},"Regional division and reduction algorithm for minimizing the sum of linear fractional functions",{"VOID":472},"10.1186\u002Fs13660-018-1651-9","https:\u002F\u002Fjournalofinequalitiesandapplications.springeropen.com\u002Farticles\u002F10.1186\u002Fs13660-018-1651-9",[475,490],{"id":476,"sortIndex":178,"researcher":18,"roles":477,"affiliations":478,"properties":487},"d435e2d4-fcd2-4947-938b-83d70f818e3f",[322],[479],{"id":18,"sortIndex":19,"affiliation":480,"properties":18},{"id":481,"createTime":482,"updateTime":482,"relativeEntities":483,"slug":18,"properties":484,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"50a025e6-937a-40c8-bb17-e0b063f68d69","2024-01-15T20:39:39.423+00:00",[],{"title":485},{"VI":486},"College of Mathematics and Information Science, Henan Normal University, Xinxiang, P.R. 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Math. Z. 39, 215-226 (1935)\nBohner, M, Peterson, A: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)\nCerone, P, Dragomir, SS: A refinement of the Grüss inequality and applications. Tamkang J. Math. 38, 37-49 (2007)\nDragomir, SS: A generalization of Grüss’s inequality in inner product spaces and applications. J. Math. Anal. Appl. 237, 74-82 (1999)\nDragomir, SS: A Grüss type discrete inequality in inner product spaces and applications. J. Math. Anal. Appl. 250, 494-511 (2000)\nLiu, Z: Notes on a Grüss type inequality and its applications. Vietnam J. Math. 35, 121-127 (2007)\nPerić, I, Rajić, R: Grüss inequality for completely bounded maps. Linear Algebra Appl. 390, 287-292 (2004)\nPečarić, JE, Tepeš, B: On the Grüss type inequalities of Dragomir and Fedotov. J. Inequal. Pure Appl. Math. 4(5), 91 (2003)\nPečarić, JE, Tepeš, B: A note on Grüss type inequality in terms of Δ-seminorms. Pril. - Maked. Akad. Nauk. Umet., Odd. Mat.-Teh. Nauki 23\u002F24 (2002\u002F2003); 29-35 (2004)\nAnastassiou, GA: Nabla Discrete fractional calculus and inequalities. arXiv:0911.3374v1 [math.CA] (2009)\nAnastassiou, GA: Multivariate Fink type identity and multivariate Ostrowski, comparison of means and Grüss type inequalities. Math. Comput. Model. 46, 351-374 (2007)\nBohner, M, Matthews, T: The Grüss inequality on time scales. Commun. Math. Anal. 3, 1-8 (2007) (electronic)\nGraham, RL, Knuth, DE, Patashnik, O: Concrete Mathematics: A Foundation for Computer Science, 2nd edn. Addison-Wesley, Reading (1994)\nMercer, AM: An improvement of the Grüss inequality. JIPAM. J. Inequal. Pure Appl. Math. 6(4), 93 (2005)\nMitrinović, DS: Analytic Inequalities. Springer, New York (1970)\nMitrinović, DS, Pečarić, JE, Fink, AM: Classical and New Inequalities in Analysis. Kluwer Academic, Dordrecht (1993)\nPachpatte, BG: Some new Ostrowski and Grüss type inequalities. Tamkang J. Math. 38(2), 11-120 (2007)\nBoros, G, Moll, V: Irresistible Integrals: Symbols, Analysis and Experiments in the Evaluation of Integrals. Cambridge University Press, Cambridge (2004)\nDiaz, JB, Osler, TJ: Differences of fractional order. Math. Comput. 28, 185-202 (1974)\nGray, HL, Zhang, NF: On a new definition of fractional difference. Math. Comput. 50, 513-529 (1988)\nAtıcı, FM, Eloe, PW: Initial value problems in discrete fractional calculus. Proc. Am. Math. Soc. 137(3), 981-989 (2009)\nAtıcı, FM, Şengül, S: Modeling with fractional difference equations. J. Math. Anal. Appl. 369(1), 1-9 (2010)\nGoodrich, CS: Continuity of solutions to discrete fractional initial value problems. Comput. Math. Appl. 59(11), 3489-3499 (2010)\nAtıcı, FM, Eloe, PW: Gronwall’s inequality on discrete fractional calculus. Comput. Math. Appl. 64(10), 3193-3200 (2012)\nAnastassiou, GA: Nabla discrete fractional calculus and nabla inequalities. Math. Comput. Model. 51(5-6), 562-571 (2010)\nGüvenilir, AF, Kaymakçalan, B, Peterson, AC, Taş, K: Nabla discrete fractional Grüss type inequality. J. Inequal. Appl. 2014, 86 (2014). doi:10.1186\u002F1029-242X-2014-86\nFerreira, RAC: A discrete fractional Gronwall inequality. Proc. Am. Math. Soc. 140(5), 1605-1612 (2012)\nAtıcı, F, Eloe, P: A transform method in discrete fractional calculus. Int. J. Difference Equ. 2, 165-176 (2007)",{"EN":547},"We give a discrete Grüss type inequality on fractional calculus.",{"EN":549},"Discrete Grüss type inequality on fractional calculus",{"VOID":551},"10.1186\u002Fs13660-015-0688-2","https:\u002F\u002Fjournalofinequalitiesandapplications.springeropen.com\u002Farticles\u002F10.1186\u002Fs13660-015-0688-2",[554,569,584,596],{"id":555,"sortIndex":395,"researcher":18,"roles":556,"affiliations":557,"properties":566},"f022a316-f39f-44c5-81a2-0061ab98d2da",[322],[558],{"id":18,"sortIndex":19,"affiliation":559,"properties":18},{"id":560,"createTime":561,"updateTime":561,"relativeEntities":562,"slug":18,"properties":563,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"cdb77dad-2303-41cb-808e-3caec86517f0","2024-01-12T16:23:29.176+00:00",[],{"title":564},{"VI":565},"Department of Mathematics and Computer Science, Çankaya University, Ankara, 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Journal of Optimization Theory and Applications 1982, 38(3):363–383. 10.1007\u002FBF00935344\nFukushima M: The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem. Mathematical Programming 1996, 72(1):1–15. 10.1007\u002FBF02592328\nHe Y: Stable pseudomonotone variational inequality in reflexive Banach spaces. Journal of Mathematical Analysis and Applications 2007, 330(1):352–363. 10.1016\u002Fj.jmaa.2006.07.063\nSaigal R: Extension of the generalized complementarity problem. Mathematics of Operations Research 1976, 1(3):260–266. 10.1287\u002Fmoor.1.3.260\nSalmon G, Strodiot J-J, Nguyen VH: A bundle method for solving variational inequalities. SIAM Journal on Optimization 2003, 14(3):869–893.\nRockafellar RT: Monotone operators and the proximal point algorithm. 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Journal of Computational and Applied Mathematics 2009, 228(1):212–218. 10.1016\u002Fj.cam.2008.09.014\nSolodov MV, Svaiter BF: A new projection method for variational inequality problems. SIAM Journal on Control and Optimization 1999, 37(3):765–776. 10.1137\u002FS0363012997317475\nFacchinei F, Pang JS: Finite-Dimensional Variational Inequalities and Complementary Problems. Springer, New York, NY, USA; 2003.\nKaramardian S: Complementarity problems over cones with monotone and pseudomonotone maps. Journal of Optimization Theory and Applications 1976, 18(4):445–454. 10.1007\u002FBF00932654\nAubin J-P, Ekeland I: Applied Nonlinear Analysis, Pure and Applied Mathematics. John Wiley & Sons, New York, NY, USA; 1984:xi+518.",{"EN":656},"We propose a new projection algorithm for generalized variational inequality with multivalued mapping. 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World J. 2014: Article ID 585964",{},{"id":918,"createTime":919,"updateTime":920,"relativeEntities":921,"slug":922,"properties":923,"entityType":202,"verifyStatus":203,"verifyTime":920,"verifyNote":204,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":932,"fullTextUrl":18,"authors":933,"publicationType":246,"publisherRelationship":1026,"citationCount":18,"citationInfo":18,"publishDate":1059,"publishYear":1060,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":18,"openAccess":18,"references":18,"isForceReanalyzing":301},"54e534df-89ad-4909-b406-f77d3b7c3e65","2024-01-18T22:27:54.381+00:00","2025-02-24T23:56:30.170+00:00",[],"On-fixed-points-of-rational-contractions-in-generalized-parametric-metric-and-fuzzy-metric-spaces",{"references":924,"abstract":926,"title":928,"doi":930},{"VOID":925},"Hussain, N., Khaleghizadeh, S., Salimi, P., Abdou, A.A.N.: A new approach to fixed point results in triangular intuitionistic fuzzy metric spaces. Abstr. Appl. Anal. 2014, Article ID 690139 (2014)\nHussain, N., Salimi, P., Parvaneh, V.: Fixed point results for various contractions in parametric and fuzzy b-metric spaces. J. Nonlinear Sci. Appl. 8, 719–739 (2015)\nTas, N., Ozgus, N.Y.: On parametric S-metric spaces and fixed point type theorems for expansive mappings. J. Math. 2016, Article ID 4746732 (2016)\nPriyobarta, N., Rohen, Y., Radenovic, S.: Fixed point theorems on parametric A-metric space. Am. J. Appl. Math. Statistics 6(1), 1–5 (2018)\nBranciari, A.: A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces. Publ. Math. (Debr.) 57, 31–37 (2000)\nSuzuki, T.: Generalized metric spaces do not have the compatible topology. Abstr. Appl. Anal. 2014, Article ID 458098 (2014)\nRao, K.P.R., Babu, D.V., Ramudu, E.T.: Some unique common fixed point theorems in parametric S-metric spaces. Int. J. Innov. Res. Sci., Eng. Technol. 3, 14375–14387 (2014)\nKrishnakumar, R., Sanatammappa, N.P.: Some fixed point theorems in parametric b-metric space. Int. J. Math. Sci. Eng. Appl. 10, 99–106 (2016)\nTas, N., Ozgur, N.Y.: Some fixed point results on parametric \\(N_{b}\\)-metric spaces. Commun. Korean Math. Soc. 33, 943–960 (2018)\nDaheriya, R.D., Shrivastava, S., Ughade, M.: Parametric metric space, parametric b-metric space and expansive type mapping. Int. J. Math. Appl. 4, 107–117 (2016)\nJain, R., Daheriya, R.D., Ughade, M.: Fixed point, coincidence point and common fixed point theorems under various expansive conditions in parametric metric spaces and parametric b-metric spaces. Gazi Univ. J. Sci. 29, 95–107 (2016)\nLikhitker, M., Daheriya, R.D., Ughade, M.: Common fixed point theorems in parametric metric spaces under nonlinear type contractions. Int. J. Math. Arch. 7, 105–109 (2016)\nPosul, H., Kutukeu, S.: On parametric spaces. Bull. Math. Stat. Res. 5, 17–20 (2017)\nTas, N., Ozgur, N.Y.: On parametric S-metric spaces and fixed point type theorems for expansive mappings. J. Math. 2016, Article ID 4746732 (2016). https:\u002F\u002Fdoi.org\u002F10.1155\u002F2016\u002F4746732\nEge, O., Karaca, I.: Fixed point theorems and an application in parametric metric space. Azerb. J. Math. 7, 27–39 (2017)\nKrishnakumar, R., Sanatammappa, N.P.: Fixed point theorems in parametric metric space. Int. J. Math. Res. 8, 213–220 (2016)\nEge, O., De le Sen, M.: A new perspective on parametric metric spaces. Mathematics 7, 1008 (2019)\nBakhru, A., Ughade, M., Gupta, R.: A new common fixed point theorem for two pairs of mappings in parametric metric space. J. Adv. Math. Comput. Sci. 35(4), 87–105 (2020)\nKataria, H.R., Patel, P.H., Shah, V.: Existence results of noninstantaneous impulsive fractional integro-differential equation. Demonstr. Math. 53, 373–384 (2020)\nVetro, F.: Fixed point for alpha-Theta-phi-contractions and first-order periodic differential problem. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 113(3), 1823–1837 (2019)\nWairojjana, N., Pakkaranang, N., Pholasa, N.: Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces. Demonstr. Math. 54, 110–128 (2021)\nRoshan, J.R., Parvaneh, V., Kadelburg, Z., Hussain, N.: New fixed point results in b-rectangular metric spaces. Nonlinear Anal., Model. Control 21(5), 614–634 (2016)\nMustafa, Z., Parvaneh, V., Jaradat, M.M.M., Kadelburg, Z.: Extended rectangular b-metric spaces and some fixed point theorems for contractive mappings. Symmetry 11(4), 594 (2019)\nLatif, A., Roshan, J.R., Parvaneh, V., Hussain, N.: Fixed point results via α-admissible mappings and cyclic contractive mappings in partial b-metric spaces. J. Inequal. Appl. 2014, 345 (2014)\nCiric, Lj., Parvaneh, V., Hussain, N.: Fixed point results for weakly α-admissible pairs. Filomat 30(14), 3697–3713 (2016)\nSamet, B., Vetro, C., Vetro, P.: Fixed point theorem for α–ψ contractive mappings. Nonlinear Anal. 75, 2154–2165 (2012)\nHussain, N., Karapinar, E., Salimi, P., Akbar, F.: α-admissible mappings and related fixed point theorems. J. Inequal. Appl. 2013, 114 (2013)\nSalimi, P., Latif, A., Hussain, N.: Modified α–ψ-contractive mappings with applications. Fixed Point Theory Appl. 2013, 151 (2013)\nAlsulami, H.H., Chandok, S., Aziz Taoudi, M., Erhan, I.M.: Some fixed point theorems for \\((\\alpha ,\\psi )\\)-rational type contractive mappings. Fixed Point Theory Appl. 2015, 97 (2015)\nAydi, H., Karapinar, E., Samet, B.: Fixed point for generalized \\((\\alpha ,\\psi )\\)-contractions on generalized metric spaces. J. Inequal. Appl. 2014, 229 (2014)\nKarapinar, E.: Discussion on \\((\\alpha ,\\psi )\\) contractions on generalized metric spaces. Abstr. Appl. Anal. 2014, Article ID 962784 (2014)\nSchweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10, 314–334 (1960)",{"EN":927},"We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for \n                \n                  \n                \n                \n                $(\\alpha ,\\psi )$\n              -rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for \n                \n                  \n                \n                \n                $(\\alpha , \\psi )$\n              -rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces.",{"EN":929},"On fixed points of rational contractions in generalized parametric metric and fuzzy metric spaces",{"VOID":931},"10.1186\u002Fs13660-021-02661-4","https:\u002F\u002Fjournalofinequalitiesandapplications.springeropen.com\u002Farticles\u002F10.1186\u002Fs13660-021-02661-4",[934,950,967,984,999,1014],{"id":935,"sortIndex":338,"researcher":18,"roles":936,"affiliations":937,"properties":947},"82f026df-faa9-495a-a161-798e78ed738e",[322],[938],{"id":18,"sortIndex":19,"affiliation":939,"properties":18},{"id":940,"createTime":941,"updateTime":941,"relativeEntities":942,"slug":943,"properties":944,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"5df49926-83a6-4824-82d6-12280d0b540e","2024-04-16T04:05:18.877+00:00",[],"Department-of-Mathematics-and-General-Sciences-Prince-Sultan-University-Riyadh-Saudi-Arabia",{"title":945},{"EN":946},"Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia",{"title":948},{"VI":949},"Nabil Mlaiki",{"id":951,"sortIndex":178,"researcher":18,"roles":952,"affiliations":953,"properties":964},"f22498b6-8358-49a9-a721-5c92947a2a20",[322],[954],{"id":18,"sortIndex":19,"affiliation":955,"properties":18},{"id":956,"createTime":957,"updateTime":958,"relativeEntities":959,"slug":960,"properties":961,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"0b4fb6c8-79f5-4262-bf44-ab4b755e3926","2024-04-06T17:10:37.244+00:00","2025-06-12T00:11:35.272+00:00",[],"Department-of-Mathematics-National-Institute-of-Technology-Manipur-Langol-India",{"title":962},{"VI":963},"Department of Mathematics, National Institute of Technology Manipur, Langol, India",{"title":965},{"VI":966},"Yumnam Rohen",{"id":968,"sortIndex":408,"researcher":18,"roles":969,"affiliations":970,"properties":981},"7608876e-555f-4e68-87dc-b79f8d2fd4bc",[322],[971],{"id":18,"sortIndex":19,"affiliation":972,"properties":18},{"id":973,"createTime":974,"updateTime":975,"relativeEntities":976,"slug":977,"properties":978,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"bfbea07a-a019-4ea0-8189-aed40c34447e","2024-01-09T09:54:24.734+00:00","2025-01-25T16:45:55.446+00:00",[],"Department-of-Mathematics-King-Abdulaziz-University-Jeddah-Saudi-Arabia",{"title":979},{"VI":980},"Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia",{"title":982},{"VI":983},"Nawab Hussain",{"id":985,"sortIndex":395,"researcher":18,"roles":986,"affiliations":987,"properties":996},"ed1df44a-3cec-48de-a4a2-1afaa4e5ebe6",[322],[988],{"id":18,"sortIndex":19,"affiliation":989,"properties":18},{"id":990,"createTime":991,"updateTime":991,"relativeEntities":992,"slug":18,"properties":993,"entityType":54,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"syncStatus":17,"languages":18,"translateLanguages":18,"viewCount":19},"78f222db-3133-4ad6-9788-d81260de4639","2024-01-18T22:27:54.435+00:00",[],{"title":994},{"VI":995},"Department of Mathematics, D. 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Positivity 20, 1–20 (2015)\nGong, X.H.: Optimality conditions for vector equilibrium problems. J. Math. Anal. Appl. 342, 1455–1466 (2008)\nGong, X.H.: Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal. TMA 73, 3598–3612 (2010)\nGong, X.H.: Efficiency and Henig efficiency for vector equilibrium problems. J. Optim. Theory Appl. 108, 139–154 (2001)\nLong, X.J., Huang, Y.Q., Peng, Z.Y.: Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints. Optim. Lett. 5, 717–728 (2011)\nQiu, Q.S.: Optimality conditions for vector equilibrium problems with constraints. J. Ind. Manag. Optim. 5, 783–790 (2017)\nLuu, D.V., Hang, D.D.: Efficient solutions and optimality conditions for vector equilibrium problems. Math. Methods Oper. Res. 79, 163–177 (2014)\nLuu, D.V.: Optimality condition for local efficient solutions of vector equilibrium problems via convexificators and applications. J. Optim. Theory Appl. 171, 643–665 (2016)\nLoridan, P.: Necessary conditions for ϵ-optimality. Math. Program. 19, 140–152 (1982)\nLoridan, P.: ϵ-solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265–276 (1984)\nLi, B.X., Li, S.J.: Continuity of approximate solution mappings for parametric equilibrium problems. J. Glob. Optim. 51, 541–548 (2011)\nYang, X.M., Li, D., Wang, S.Y.: Near-subconvexlikeness in vector optimization with set-valued functions. J. Optim. Theory Appl. 110, 413–427 (2001)\nSach, P.H.: New generalized convexity notion for set-valued maps and application to vector optimization. J. Optim. Theory Appl. 125, 157–179 (2005)\nXu, Y.H., Song, X.S.: The relationship between ic-cone-convexness and nearly cone-subconvexlikeness. Appl. Math. Lett. 24, 1622–1624 (2011)\nRong, W.D., Wu, Y.N.: ϵ-weak minimal solutions of vector optimization problems with set-valued maps. J. Optim. Theory Appl. 106, 569–579 (2000)\nLi, Z.F., Chen, G.Y.: Lagrangian multipliers, saddle points, and duality in vector optimization of set-valued maps. J. Math. Anal. Appl. 215, 279–316 (1997)\nYang, X.M., Yang, X.Q., Chen, G.Y.: Theorems of the alternative and optimization with set-valued maps. J. Optim. Theory Appl. 107, 627–640 (2000)\nSach, P.H.: Nearly subconvexlike set-valued maps and vector optimization problems. J. Optim. Theory Appl. 119, 335–356 (2003)",{"EN":1069},"In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly efficient solutions and approximate weakly efficient solutions. 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C: A Schwarz inequality for convex operator functions. Proc. Am. Math. Soc. 1957, 8: 42–44. 10.1090\u002FS0002-9939-1957-0084120-4\nChoi MD:A Schwarz inequality for positive linear maps on C ∗ -algebras. Ill. J. Math. 1974, 18: 565–574.\nHansen F, Pedersen GK: Jensen’s inequality for operators and Löwner’s theorem. Math. Ann. 1982, 258: 229–241. 10.1007\u002FBF01450679\nHansen F, Pedersen GK: Jensen’s operator inequality. Bull. Lond. Math. Soc. 2003, 35: 553–564. 10.1112\u002FS0024609303002200\nMond B, Pečarić J: On Jensen’s inequality for operator convex functions. Houst. J. Math. 1995, 21: 739–754.\nFuruta T, Mićić Hot J, Pečarić J, Seo Y Monographs in Inequalities 1. In Mond-Pečarić Method in Operator Inequalities. Element, Zagreb; 2005.\nHansen F, Pečarić J, Perić I: Jensen’s operator inequality and its converses. Math. Scand. 2007, 100: 61–73.\nAbramovich S, Jameson G, Sinnamon G: Refining Jensen’s inequality. Bull. Math. Soc. Sci. Math. Roum. 2004, 47: 3–14.\nDragomir SS: A new refinement of Jensen’s inequality in linear spaces with applications. Math. Comput. Model. 2010, 52: 1497–1505. 10.1016\u002Fj.mcm.2010.05.035\nFujii JI: An external version of the Jensen operator inequality. Sci. Math. Japon. Online 2011, 2011: 59–62.\nFujii JI, Pečarić J, Seo Y: The Jensen inequality in an external formula. J. Math. Inequal. 2012, 6: 473–480.\nIvelić A, Matković A, Pečarić JE: On a Jensen-Mercer operator inequality. Banach J. Math. Anal. 2011, 5: 19–28.\nKhosravi M, Aujla JS, Dragomir SS, Moslehian MS: Refinements of Choi-Davis-Jensen’s inequality. Bull. Math. Anal. Appl. 2011, 3: 127–133.\nMićić J, Pavić Z, Pečarić J: Extension of Jensen’s operator inequality for operators without operator convexity. Abstr. Appl. Anal. 2011, 2011: 1–14.\nMićić J, Pečarić J, Perić J: Extension of the refined Jensen’s operator inequality with condition on spectra. Ann. Funct. Anal. 2012, 3: 67–85.\nMoslehian MS, Kian M: Jensen type inequalities for Q -class functions. Bull. Aust. Math. Soc. 2011, 85: 128–142.\nRooin J: A refinement of Jensen’s inequality. J. Inequal. Pure Appl. Math. 2005., 6(2): Article ID 38\nSrivastava HM, Xia ZG, Zhang ZH: Some further refinements and extensions of the Hermite-Hadamard and Jensen inequalities in several variables. Math. Comput. Model. 2011, 54: 2709–2717. 10.1016\u002Fj.mcm.2011.06.057\nXiao ZG, Srivastava HM, Zhang ZH: Further refinements of the Jensen inequalities based upon samples with repetitions. Math. Comput. Model. 2010, 51: 592–600. 10.1016\u002Fj.mcm.2009.11.004\nWang LC, Ma XF, Liu LH: A note on some new refinements of Jensen’s inequality for convex functions. J. Inequal. Pure Appl. Math. 2009., 10(2): Article ID 48\nMićić J, Pavić Z, Pečarić J: Jensen’s inequality for operators without operator convexity. Linear Algebra Appl. 2011, 434: 1228–1237. 10.1016\u002Fj.laa.2010.11.004\nMićić J, Pečarić J, Perić J: Refined Jensen’s operator inequality with condition on spectra. Oper. Matrices 2013, 7: 293–308.\nMond B, Pečarić JE: Converses of Jensen’s inequality for linear maps of operators. An. Univ. Timiş., Ser. Mat.-Inform. 1993, 2: 223–228.\nMond B, Pečarić J: Converses of Jensen’s inequality for several operators. Rev. Anal. Numér. Théor. Approx. 1994, 23: 179–183.\nFuruta T: Operator inequalities associated with Hölder-McCarthy and Kantorovich inequalities. J. Inequal. Appl. 1998, 2: 137–148.\nMićić J, Seo Y, Takahasi SE, Tominaga M: Inequalities of Furuta and Mond-Pečarić. Math. Inequal. Appl. 1999, 2: 83–111.\nMićić J, Pečarić J, Seo Y, Tominaga M: Inequalities of positive linear maps on Hermitian matrices. Math. Inequal. Appl. 2000, 3: 559–591.\nMićić J, Pečarić J, Seo Y: Converses of Jensen’s operator inequality. Oper. Matrices 2010, 4: 385–403.\nMićić J, Pavić Z, Pečarić J: Some better bounds in converses of the Jensen operator inequality. Oper. Matrices 2012, 6: 589–605.\nMitrinović DS, Pečarić JE, Fink AM: Classical and New Inequalities in Analysis. Kluwer Academic, Dordrecht; 1993.",{"EN":1158},"In this paper converses of a generalized Jensen’s inequality for a continuous field of self-adjoint operators, a unital field of positive linear mappings and real-valued continuous convex functions are studied. New refined converses are presented by using the Mond-Pečarić method improvement. Obtained results are applied to refine selected inequalities with power functions. 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S: Linear 2-normierte Räume. Math. Nachr. 1965, 28: 1–43.\nMisiak A: n -Inner product spaces. Math. Nachr. 1989, 140: 299–319. 10.1002\u002Fmana.19891400121\nGunawan H: On n -inner product, n -norms, and the Cauchy-Schwartz inequality. Sci. Math. Jpn. 2001, 5: 47–54.\nGunawan H: The space of p -summable sequence and its natural n -norm. Bull. Aust. Math. Soc. 2001, 64: 137–147. 10.1017\u002FS0004972700019754\nGunawan H, Mashadi M: On n -normed spaces. Int. J. Math. Math. Sci. 2001, 27: 631–639. 10.1155\u002FS0161171201010675\nHardy GH: On the convergence of certain multiple series. Proc. Camb. Philos. Soc. 1917, 19: 86–95.\nBromwich TJ: An Introduction to the Theory of Infinite Series. Macmillan & Co., New York; 1965.\nMóricz F: Extension of the spaces c and c 0 from single to double sequences. Acta Math. Hung. 1991, 57: 129–136. 10.1007\u002FBF01903811\nMóricz F, Rhoades BE: Almost convergence of double sequences and strong regularity of summability matrices. Math. Proc. Camb. Philos. Soc. 1988, 104: 283–294. 10.1017\u002FS0305004100065464\nBaşarır M, Sonalcan O: On some double sequence spaces. J. Indian Acad. Math. 1999, 21: 193–200.\nMursaleen M, Mohiuddine SA: Regularly σ -conservative and σ -coercive four dimensional matrices. Comput. Math. Appl. 2008, 56: 1580–1586. 10.1016\u002Fj.camwa.2008.03.007\nMursaleen M, Mohiuddine SA: On σ -conservative and boundedly σ -conservative four-dimensional matrices. Comput. Math. Appl. 2010, 59: 880–885. 10.1016\u002Fj.camwa.2009.10.006\nMursaleen M: Almost strongly regular matrices and a core theorem for double sequences. J. Math. Anal. Appl. 2004,293(2):523–531. 10.1016\u002Fj.jmaa.2004.01.014\nMursaleen M, Edely OHH: Almost convergence and a core theorem for double sequences. J. Math. Anal. Appl. 2004,293(2):532–540. 10.1016\u002Fj.jmaa.2004.01.015\nAltay B, Başar F: Some new spaces of double sequences. J. Math. Anal. Appl. 2005, 309: 70–90. 10.1016\u002Fj.jmaa.2004.12.020\nBaşar F, Sever Y:The space L q of double sequences. Math. J. Okayama Univ. 2009, 51: 149–157.\nMursaleen M, Mohiuddine SA: Some matrix transformations of convex and paranormed sequence spaces into the spaces of invariant means. J. Funct. Spaces Appl. 2012., 2012: Article ID 612671\nMohiuddine SA, Alotaibi A: Some spaces of double sequences obtained through invariant mean and related concepts. Abstr. Appl. Anal. 2013., 2013: Article ID 507950\nDemirci K: Strong A -summability and A -statistical convergence. Indian J. Pure Appl. Math. 1996, 27: 589–593.\nMursaleen M, Mohiuddine SA: Some new double sequences spaces of invariant means. Glas. Mat. 2010,45(65):139–153.\nParashar SD, Choudhary B: Sequence spaces defined by Orlicz functions. Indian J. Pure Appl. Math. 1994, 25: 419–428.\nKizmaz H: On certain sequences spaces. Can. Math. Bull. 1981,24(2):169–176. 10.4153\u002FCMB-1981-027-5\nEt M, Çolak R: On generalized difference sequence spaces. Soochow J. Math. 1995,21(4):377–386.\nEt M: Spaces of Cesàro difference sequences of order r defined by a modulus function in a locally convex space. Taiwan. J. Math. 2006,10(4):865–879.\nEt M: Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences. Appl. Math. Comput. 2013, 219: 9372–9376. 10.1016\u002Fj.amc.2013.03.039\nRaj K, Sharma AK, Sharma SK: A sequence space defined by Musielak-Orlicz function. Int. J. Pure Appl. Math. 2011, 67: 475–484.\nRaj K, Jamwal S, Sharma SK: New classes of generalized sequence spaces defined by an Orlicz function. J. Comput. Anal. Appl. 2013, 15: 730–737.\nRaj K, Sharma SK: Some generalized difference double sequence spaces defined by a sequence of Orlicz-function. CUBO 2012, 14: 167–189. 10.4067\u002FS0719-06462012000300011\nRaj K, Sharma SK, Sharma AK: Some difference sequence spaces in n -normed spaces defined by Musielak-Orlicz function. Armen. J. Math. 2010, 3: 127–141.\nTripathy BC: Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces. Soochow J. Math. 2004, 30: 431–446.\nEt M, Altin Y, Choudhary B, Tripathy BC: On some classes of sequences defined by sequences of Orlicz functions. Math. Inequal. Appl. 2006, 9: 335–342.\nLindenstrauss J, Tzafriri L: On Orlicz sequence spaces. Isr. J. Math. 1971, 10: 379–390. 10.1007\u002FBF02771656\nMaligranda L Seminars in Mathematics 5. Orlicz Spaces and Interpolation 1989. Polish Academy of Science\nMusielak J Lecture Notes in Mathematics 1034. In Orlicz Spaces and Modular Spaces. Springer, Berlin; 1983.\nPringsheim A: Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 1900, 53: 289–321. 10.1007\u002FBF01448977\nCooke RG: Infinite Matrices and Sequence Spaces. Macmillan & Co., London; 1950.\nRobison GM: Divergent double sequences and series. Trans. Am. Math. Soc. 1926, 28: 50–73. 10.1090\u002FS0002-9947-1926-1501332-5\nHamilton HJ: Transformation of multiple sequences. Duke Math. J. 1936, 2: 29–60. 10.1215\u002FS0012-7094-36-00204-1\nMaddox IJ: Elements of Functional Analysis. 2nd edition. Cambridge University Press, Cambridge; 1988.\nSimons S:The sequence spaces l( p v ) and m( p v ) . Proc. Lond. Math. Soc. 1965,15(3):422–436.\nYurdakadim T, Tas E: Double sequences and Orlicz functions. Period. Math. Hung. 2013, 67: 47–54. 10.1007\u002Fs10998-013-6362-x\nMohiuddine SA, Raj K, Alotaibi A: Some paranormed double difference sequence spaces for Orlicz functions and bounded-regular matrices. Abstr. Appl. Anal. 2014., 2014: Article ID 419064",{"EN":1253},"The aim of this paper is to introduce some generalized spaces of double sequences with the help of the Musielak-Orlicz function \n                  \n                    \n                  \n                  \n                    \n                  \n                 and four-dimensional bounded-regular (shortly, RH-regular) matrices \n                  \n                    \n                  \n                  \n                    \n                  \n                 over n-normed spaces. Some topological properties and inclusion relations between these spaces are investigated. 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