Existence and uniqueness of fixed point on closed ball in multiplicative $\mathbf{G}_\mathcal{M}-$metric space

TL;DR

This paper establishes new fixed point theorems in ordered complete multiplicative G_M-metric spaces under generalized contractive conditions, broadening the theoretical framework for such spaces.

Contribution

It introduces new definitions and fixed point results in ordered complete multiplicative G_M-metric spaces, including generalized Δ-implicit contractive conditions.

Findings

Proved existence and uniqueness of fixed points under new conditions

Presented illustrative examples validating the theorems

Extended fixed point theory in multiplicative G_M-metric spaces

Abstract

In this article, we investigate some fixed point results satisfying a new generalized $\Delta$-implicit contractive condition in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Also, some new definitions and fixed point theorems are presented in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Furthermore, some nontrivial and illustrative examples are given to validate our obtained results.