Some outcomes of fixed Point theorems pertaining to C-Class Functions within G-Metric Spaces

Abstract

We demonstrate that there is and only is one self-mapping  that satisfies a contractive condition under the management of three control functions  and an auxiliary function  using Ansari’s -class function [1] and Khan, Swaleh, and Sessa’s altering distance functions [11]. This study presents a -metric counterpart to Huang, Deng, and Radenović’s -metric results [10]. The proof relies on a contradiction argument to control the auxiliary functions  along the Picard sequence, as the rectangle inequality of a -metric does not carry a multiplicative coefficient, unlike the triangle inequality of a -metric. We construct several corollaries that recover classical contraction-type theorems, provide an example, as well as how to apply them to the problem of finding a unique solution to a nonlinear integral equation.