Theoretical approaches for generalized proximal Z-contraction maps in b-metric spaces with applications
Abstract
This paper explores the simulation function and the concept of Z-contraction concerning ζ, which serve as a generalization of the Banach contraction principle. These ideas unify various existing contraction types by incorporating both d(Ta,Tb) and d(a,b). Our findings extend and generalize the work of Olgun et al. [27], Abbas et al. [1], and Goswami et al. [21], transitioning from metric spaces to the framework of b-metric spaces. We propose the concept of a generalized proximal Z-contraction for pairs of non-self mappings and demonstrate the existence and uniqueness of common best proximity points in complete b-metric spaces. Additionally, we present supporting examples and illustrate some applications of our findings.
Copyright © 2025 Dasari Ratna Babu, Naga Koteswara Rao Koduru, Chinni Suresh, Sowjanya Kuchibhotla, P. Sudheer Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. R. Babu, N. K. R. Koduru, C. Suresh, S. Kuchibhotla, P. S. Kumar, Theoretical approaches for generalized proximal Z-contraction maps in b-metric spaces with applications, Adv. Fixed Point Theory 15 (2025), 38. https://doi.org/10.28919/afpt/9497
BibTeX
@article{Babu2025,
author = {Babu, Dasari Ratna and Koduru, Naga Koteswara Rao and Suresh, Chinni and Kuchibhotla, Sowjanya and Kumar, P. Sudheer},
title = {Theoretical approaches for generalized proximal Z-contraction maps in b-metric spaces with applications},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {38},
doi = {10.28919/afpt/9497}
}