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In this article, we investigate some fixed point results satisfying a newgeneralized $\Delta$-implicit contractive condition in ordered completemultiplicative $\mathbf{G}_\mathcal{M}-$metric space. Also, some newdefinitions and fixed point theorems are presented in ordered completemultiplicative $\mathbf{G}_\mathcal{M}-$metric space. Furthermore, somenontrivial and illustrative examples are given to validate our obtainedresults.

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