Fixed point theory in multiplicative metric space and its application in boundary value problems and cyclic mappings
Abstract
In this paper, building on the recent work of Stojan Radenović and Bessem Samet, we establish several fixed point theorems in multiplicative metric spaces for Jaggi-type and weak contractions. These results are derived using a function \(\varphi: [1, \infty) \to [0, \infty)\) satisfying \(\varphi(s) \ge b (\ln s)^c\) for \(s > 1\), with \(b\) and \(c\) positive constants. The theorems presented here are not equivalent to their classical analogues in standard metric spaces. To demonstrate the applicability of our results, we provide an example involving a boundary value problem for a second-order differential equation and the determination of a unique fixed point for a cyclic mapping.
Copyright © 2026 Sagolsem Yaikhonba Meetei, Yumnam Mahendra Singh, Irom Shashikanta Singh. 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
S. Y. Meetei, Y. M. Singh, I. S. Singh, Fixed point theory in multiplicative metric space and its application in boundary value problems and cyclic mappings, Adv. Fixed Point Theory 16 (2026), 23. https://doi.org/10.28919/afpt/9915
BibTeX
@article{Meetei2026,
author = {Meetei, Sagolsem Yaikhonba and Singh, Yumnam Mahendra and Singh, Irom Shashikanta},
title = {Fixed point theory in multiplicative metric space and its application in boundary value problems and cyclic mappings},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {23},
doi = {10.28919/afpt/9915}
}