On the fractional integral inclusions having exponential kernels for interval-valued convex functions

Mathematical Sciences - Tập 17 Số 2 - Trang 107-120 - 2023
Taichun Zhou1, Zhengrong Yuan1, Tingsong Du1
1Department of Mathematics, College of Science, China Three Gorges University, Yichang, People’s Republic of China

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Abramovich, S., Persson, L.E.: Fejér and Hermite–Hadamard type inequalities for $$N$$-quasi-convex functions. Math. Notes 102, 599–609 (2017)

Ahmad, B., Alsaedi, A., Kirane, M., Torebek, B.T.: Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals. J. Comput. Appl. Math. 353, 120–129 (2019)

Breckner, W.W.: Continuity of generalized convex and generalized concave set-valued functions. Rev. Anal. Numér. Théor. Approx. 22, 39–51 (1993)

Budak, H., Tunç, T., Sarikaya, M.Z.: Fractional Hermite–Hadamard-type inequalities for interval-valued functions. Proc. Am. Math. Soc. 148, 705–718 (2020)

Chen, H., Katugampola, U.N.: Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals. J. Math. Anal. Appl. 446, 1274–1291 (2017)

Delavar, M.R., De La Sen, M.: A mapping associated to $$h$$-convex version of the Hermite–Hadamard inequality with applications. J. Math. Inequal. 14, 329–335 (2020)

Du, T.S., Luo, C.Y., Yu, B.: Certain quantum estimates on the parameterized integral inequalities and their applications. J. Math. Inequal. 15, 201–228 (2021)

Du, T.S., Awan, M.U., Kashuri, A., Zhao, S.S.: Some $$k$$-fractional extensions of the trapezium inequalities through generalized relative semi-$$(m, h)$$-preinvexity. Appl. Anal. 100, 642–662 (2021)

Du, T.S., Wang, H., Khan, M.A., Zhang, Y.: Certain integral inequalities considering generalized $$m$$-convexity on fractal sets and their applications. Fractals 27, 1–17 (2019)

Ghosh, D., Debnath, A.K., Pedrycz, W.: A variable and a fixed ordering of intervals and their application in optimization with interval-valued functions. Int. J. Approx. Reason. 121, 187–205 (2020)

İşcan, İ: Weighted Hermite–Hadamard–Mercer type inequalities for convex functions. Numer. Methods Part. Differ. Equ. 37, 118–130 (2021)

Kadakal, H., Bekar, K.: New inequalities for $$AH$$-convex functions using beta and hypergeometric functions. Poincare J. Anal. Appl. 2, 105–114 (2019)

Kadakal, M., Karaca, H., İşcan, İ: Hermite-Hadamard type inequalities for multiplicatively geometrically $$P$$-functions. Poincare J. Anal. Appl. 2, 77–85 (2018)

Khan, M. A., Ali, T., Dragomir, S. S., Sarikaya, M. Z.: Hermite–Hadamard type inequalities for conformable fractional integrals. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 112, 1033–1048 (2018)

Kórus, P.: An extension of the Hermite–Hadamard inequality for convex and $$s$$-convex functions. Aequ. Math. 93, 527–534 (2019)

Kunt, M., İşcan, İ, Turhan, S., Karapinar, D.: Improvement of fractional Hermite–Hadamard type inequality for convex functions. Miskolc Math. Notes 19, 1007–1017 (2018)

Marinescu, D.Ş, Monea, M.: A very short proof of the Hermite–Hadamard inequalities. Am. Math. Month. 127, 850–851 (2020)

Mehrez, K., Agarwal, P.: New Hermite-Hadamard type integral inequalities for convex functions and their applications. J. Comput. Appl. Math. 350, 274–285 (2019)

Mohammed, P.O.: Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals of a convex function with respect to a monotone function. Math. Methods Appl. Sci. 44, 2314–2324 (2021)

Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2009)

Pachpatte, B.G.: On some inequalities for convex functions. RGMIA Res. Rep. Collect. E 6 (2003) (Online). https://rgmia.org/papers/v6e/convex1.pdf

Román-Flores, H., Chalco-Cano, Y., Lodwick, W.A.: Some integral inequalities for interval-valued functions. Comput. Appl. Math. 37, 1306–1318 (2018)

Rothwell, E.J., Cloud, M.J.: Automatic error analysis using intervals. IEEE Trans. Ed. 55, 9–15 (2012)

Sadowska, E.: Hadamard inequality and a refinement of Jensen inequality for set-valued functions. Result Math. 32, 332–337 (1997)

Set, E., Butt, S.I., Akdemir, A.O., Karaoǧlan, A., Abdeljawad, T.: New integral inequalities for differentiable convex functions via Atangana–Baleanu fractional integral operators. Chaos, Solitons and Fractals 143, 110554 (2021)

Singh, D., Dar, B.A., Kim, D.S.: KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions. Eur. J. Oper. Res. 254, 29–39 (2016)

Snyder, J.M.: Interval analysis for computer graphics. SIGGRAPH Comput. Graph. 26, 121–130 (1992)

de Weerdt, E., Chu, Q.P., Mulder, J.A.: Neural network output optimization using interval analysis. IEEE Trans. Neural Netw. 20, 638–653 (2009)

Younus, A., Nisar, O.: Convex optimization of interval valued functions on mixed domains. Filomat 33, 1715–1725 (2019)

Zhao, D.F., An, T.Q., Ye, G.J., Torres, D.F.M.: On Hermite–Hadamard type inequalities for harmonical $$h$$-convex interval-valued functions. Math. Inequal. Appl. 23, 95–105 (2020)

Zhao, D.F., An, T.Q., Ye, G.J., Liu, W.: New Jensen and Hermite–Hadamard type inequalities for $$h$$-convex interval-valued functions. J. Inequal. Appl. 2018, 302 (2018)