Generalized multiplicative nonlinear elastic matching distance measure and fixed point approximation

Abstract

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

Editorial of the special issue on modelling, analysis, and applications

“…The optimal common solution is achieved through an inertial parallel hybrid algorithm, under a suitable set of control conditions. Another paper proposes a $$$ {b}_g $$$‐multiplicative metric space, inspired by the concept of nonlinear elastic matching, generalized metrics, and multiplicative triangle inequality, to generalize the distance between 2 points and $$$ G $$$‐metric between 3 points [36]. Additionally, a study applies interpolation techniques to create an environment for the existence of fixed point and circle and to solve a two‐point boundary value problem, associated to a differential equation of second order [37].…”