Some fixed point theorems for (ξ,α)-expansive mappings in complete bipolar metric spaces
Resumo
In this paper, we will introduce the notion of (ξ,α)-expansive covariant and contravariant mappings in bipolar metric spaces. In addition, we prove some fixed point theorems for existence and uniqueness of fixed points for (ξ,α)-expansive covariant and contravariant mappings in complete bipolar metric space. At the end, we shall also provide some examples to support the theorems.
Downloads
Referências
Banach S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae 3, 133-181,(1922).
Border K. C., Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge (1990).
Chen C. M., Chang T. H., A common fixed point theorem for the ψ -contractive mapping, Tamkang journal of mathematics, 41(1), 25-30, (2010) .
Kang S. M., Fixed points for expansion mappings, Math. Jpn., 38, 713-717, (1993).
Mutlu A., Gurdal U., Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9(9), 5362-5373, (2016).
Mutlu A., Gurdal U., Ozkan K., Fixed point results for α − ψ-contractive mappings in bipolar metric spaces, Journal of Inequalities and Special Functions, 11(1), 64-75, (2020).
Mutlu A., Gurdal U., Ozkan K., Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, 21, 271-280, (2020).
Mutlu A., Ozkan K., Gurdal U., Coupled Fixed Point Theorems on Bipolar Metric Spaces, EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 10(4), 655-667, (2017).
Rhoades B. E., A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc., 226, 257-290, (1977).
Shahi P., Kaur J., Bhatia S.S., Fixed point theorems for (α, ξ)- expansive mappings in complete metric spaces, Fixed Point Theory and Applications, 157(1), 1-2, (2012).
Taniguchi T., Common fixed point theorems on expansion type mappings on complete metric spaces, Math. Jpn., 34, 139-142, (1989).
Wang S. Z., Li B. Y., Gao Z. M., Iseki K., Some fixed point theorems on expansion mappings, Math. Jpn., 29, 631-636, (1984).
Zeidler E., Nonlinear Functional Analysis and its Applications, Springer”, New York, (1989).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).



