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

Mohamed Gamal, Fu-Gui Shi

Published 2022-06-13Version 1

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.