ADVANCED FIXED POINT THEOREMS IN b?METRIC LIKE SPACES WITH ANALYTICAL AND NUMERICAL APPLICATIONS

Abstract

This paper introduces several novel fixed point theorems for self-mappings defined on complete b-metric-like spaces. The main results establish the existence and unique-ness of fixed points under new generalized rational-type contractive conditions which significantly extend and refine classical results by relaxing standard metric assumptions. Thetheoretical power of these theorems is demonstrated through a non-trivial application: weprove the existence of a unique solution for a nonlinear Fredholm integral equation with a nonlinear kernel. Furthermore, the convergence behavior of the associated iterative schemeis validated numerically. Our findings, supported by surface plots and computational evi-dence, underscore the efficacy of b-metric-like spaces in fixed point theory and their potentialfor solving complex integral equations.