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

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

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).