Abstract
Abstract The objective of this manuscript is to introduce the notion of multiplicative đȘ {\mathfrak{m}} -metric space, inspired by the concepts of multiplicative metric space and đȘ {\mathfrak{m}} -metric space. We propose a generalized notion of the distance function known as the multiplicative đȘ {\mathfrak{m}} -metric. Firstly, we present the fundamental definitions for the multiplicative đȘ {\mathfrak{m}} -metric space, then delve into the topological aspects, including the convergence of sequences and completeness. Additionally, we provide various illustrations to support our discussion. We also generalize some well-known contraction mappings and prove fixed point theorems on the complete multiplicative đȘ {\mathfrak{m}} -metric space. To complement our findings, we have included numerical results along with graphs to provide visual support for our conclusions. Furthermore, we explore the potential of utilizing the multiplicative đȘ {\mathfrak{m}} -metric to demonstrate the existence of the solution to a multiplicative integral equation.
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