Generalized multiplicative nonlinear elastic matching distance measure and fixed point approximation

What is it about?

In this paper, inspired by the concept of nonlinear elastic matching, generalized metrics, and multiplicative triangle inequality, we propose a bg‐multiplicative metric space in which we propose a generalized notion of a distance function, bg, with degree 2 is a distance of 3 points in generalizing the ordinary distance between 2 points and G‐metric between 3 points. We first discuss bg‐multiplicative metric space mapping and later on the fundamental properties of bg‐multiplicative metric are also discussed. Fundamental properties and several examples for the bg‐multiplicative metric are also given. Moreover, topological properties of the bg‐multiplicative metric space including the convergence of sequences and the continuity of mappings on the bg‐multiplicative metric space are studied. Finally, we generalize some well‐known fixed point theorems including Banach contraction mapping as bg‐multiplicative contraction mapping, and proved some fixed point theorems on complete bg‐multiplicative metric spaces. We prove the existence and uniqueness of a solution to a system of bg‐multiplicative integral equations as an application. Our results generalize many pre‐existing results in the literature.

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Photo by Sean Sinclair on Unsplash

Photo by Sean Sinclair on Unsplash

Why is it important?

To understand the topological properties of b-metric spaces, G-metric spaces, and Multiplicative metric spaces altogether.

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