Equivalence of some results and fixed-point theorems in S-multiplicative metric spaces

Olusola Kayode Adewale1, Samuel Olusola Ayodele1, Babatunde Eriwa Oyelade2, Emmanuella Ehui Aribike3
1Tai Solarin University of Education, Ogun State, Nigeria
2Bowling Green State University, Ohio, United States
3Lagos State University of Science and Technology, Ikorodu, Nigeria

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)