Equivalence of some results and fixed-point theorems in S-multiplicative metric spaces
Tóm tắt
In this paper, some fixed-point theorems are stated and proved in S-multiplicative metric spaces. We also show in this paper that some fixed-point results for various S-multiplicative metric spaces are equivalent to those of corresponding fixed-point results in S-metric spaces. Some examples are presented to validate the originality and applicability of our main results.
Tài liệu tham khảo
Adewale, O.K., Iluno, C.: Fixed point theorems on rectangular S-metric spaces. Sci. Afr. 16, 1–10 (2022)
Adewale, O.K., Olaleru, J.O., Akewe, H.: Fixed point theorems of Zamfirescu’s type in complex valued Gb-metric spaces. Trans. Niger. Assoc. Math. Phys. 8(1), 5–10 (2019)
Adewale, O.K., Olaleru, J.O., Akewe, H.: Fixed point theorems on a quaternion valued G-metric spaces. Commun. Nonlinear Anal. 7, 73–81 (2019)
Adewale, O.K., Olaleru, J.O., Olaoluwa, H., Akewe, H.: Fixed point theorems on a γ-generalized quasi-metric spaces. Creative Math. Inform. 28, 135–142 (2019)
Adewale, O.K., Osawaru, K.: G-cone metric spaces over Banach algebras and some fixed point results. Int. J. Math. Anal. Optim. 2019(2), 546–557 (2019)
Adewale, O.K., Umudu, J.C., Mogbademu, A.A.: Fixed point theorems on \(A_{p}\)-metric spaces with an application. Int. J. Math. Anal. Optim. 2020(1), 657–668 (2020)
Ansari, A.H., Ege, O., Radenovic, S.: Some fixed point results on complex valued Gb-metric spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112(2), 463–472 (2018)
Banach, S.: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundam. Math., 133–181 (1922)
Bashirov, A., Kurpinar, E., Ozyapici, A.: Multiplicative calculus and its applications. J. Math. Anal. Appl. 337(1), 36–48 (2008)
Branciari, A.: A fixed point theorem of Banach–Caccippoli type on a class of generalized metric spaces. Publ. Math. (Debr.) 57, 31–37 (2000)
Dhage, B.C.: Generalized metric space and mapping with fixed point. Bull. Calcutta Math. Soc. 84, 329–336 (1992)
Ege, O.: Complex valued rectangular b-metric spaces and an application to linear equations. J. Nonlinear Sci. Appl. 8(6), 1014–1021 (2015)
Ege, O.: Complex valued Gb-metric spaces. J. Comput. Anal. Appl. 21(2), 363–368 (2016)
Ege, O.: Some fixed point theorems in complex valued Gb-metric spaces. J. Nonlinear Convex Anal. 18(11), 1997–2005 (2017)
Ege, O., Karaca, I.: Common fixed point results on complex valued Gb-metric spaces. Thai J. Math. 16(3), 775–787 (2018)
Ege, O., Park, C., Ansari, A.H.: A different approach to complex valued Gb-metric spaces. Adv. Differ. Equ. 152, 1–13 (2020). https://doi.org/10.1186/s13662-020-02605-0
Frechet, M.: Sur quelques points du calcul fonctionnel. Rend. Circ. Mat. Palermo 22, 1–72 (1906)
Gahler, S.: 2-Metrische Raume und ihre topologische Struktur. Math. Nachr. 26, 115–148 (1963)
Gholidahneh, A., Sedghi, S., Ege, O., Mitrovic, Z.D., De la Sen, M.: The Meir–Keeler type contractions in extended modular b-metric spaces with an application. AIMS Math. 6(2), 1781–1799 (2021)
Iqbal, M., Batool, A., Ege, O., De la Sen, M.: Fixed point of almost contraction in b-metric spaces. J. Math. 3218134, 1–6 (2020). https://doi.org/10.1155/2020/3218134
Isik, H., Mohammadi, B., Parvaneh, V., Park, C.: Extended quasi b-metric-like spaces and some fixed point theorems for contractive mappings. Appl. Math. E-Notes 20, 204–214 (2020)
Kannan, R.: Some results on fixed points. Bull. Calcutta Math. Soc. 10, 71–76 (1968)
Mitrovic, Z.D., Isik, H., Radenovic, S.: The new results in extended b-metric spaces and applications. Int. J. Nonlinear Anal. Appl. 11(1), 473–482 (2020)
Mustafa, Z., Shahkoohi, R.J., Parvaneh, V., Kadelburg, Z., Jaradat, M.M.M.: Ordered \(S_{p}\)-metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems. Fixed Point Theory Appl. 2019, Article ID 16 (2019)
Mustafa, Z., Sims, B.: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7, 289–297 (2006)
Olaleru, J.O.: Common fixed points of three self-mappings in cone metric spaces. Appl. Math. E-Notes 11, 41–49 (2009)
Olaleru, J.O., Samet, B.: Some fixed point theorems in cone rectangular metric spaces. J. Niger. Math. Soc. 33, 145–158 (2014)
Santosh, K., Terentius, R.: Fixed points for non-self mappings in multiplicative metric spaces. Malaya J. Mat. 6(4), 800–806 (2018)
Sedghi, S., Shobe, N., Aliouche, A.: A generalization of fixed point theorem in S-metric spaces. Mat. Vesn. 64, 258–266 (2012)
Sedghi, S., Shobe, N., Zhou, H.: A common fixed point theorem in D*-metric spaces. Fixed Point Theory Appl. 2007, Article ID 027906 (2007)
Terentius, R., Santosh, K.: Fixed point theorems for non-self mappings in multiplicative metric spaces. Konuralp J. Math. 8(1), 1–6 (2020)
Zamfirescu, T.: Fixed point theorems in metric spaces. Arch. Math. Log. 23, 292–298 (1972)