Some approximate best proximity point results on metric spaces and its applications
Abstract
The aim of this paper is to extend the concept of determining an approximate fixed points (AFP) to determine approximate best proximity points (ABPP) using several contraction mappings, such as weak contraction, Zamfirescu contraction, Ciric-Reich-Rus contraction and the related consequences in metric spaces. In particular, we study the existence (qualitative results) and the diameter (quantitative results) of ABPP on metric spaces. Moreover, a few examples are provided to illustrate our results. Furthermore, suitable applications of the main findings are discussed in the domain of differential equations.
Copyright © 2026 P. Mayavel, K. Sujatha, K. Suresh, R. Theivaraman. 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
P. Mayavel, K. Sujatha, K. Suresh, R. Theivaraman, Some approximate best proximity point results on metric spaces and its applications, Adv. Fixed Point Theory 16 (2026), 14. https://doi.org/10.28919/afpt/9800
BibTeX
@article{Mayavel2026,
author = {Mayavel, P. and Sujatha, K. and Suresh, K. and Theivaraman, R.},
title = {Some approximate best proximity point results on metric spaces and its applications},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {14},
doi = {10.28919/afpt/9800}
}