Multiplicative 𝔪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results

Abstract

Abstract The objective of this manuscript is to introduce the notion of multiplicative 𝔪 {\mathfrak{m}} -metric space, inspired by the concepts of multiplicative metric space and 𝔪 {\mathfrak{m}} -metric space. We propose a generalized notion of the distance function known as the multiplicative 𝔪 {\mathfrak{m}} -metric. Firstly, we present the fundamental definitions for the multiplicative 𝔪 {\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 𝔪 {\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 𝔪 {\mathfrak{m}} -metric to demonstrate the existence of the solution to a multiplicative integral equation.