Theorems on Common Coupled Fixed Point in C*-Algebra Valued Rectangular Parametric Metric Space

Abstract

In this work, we establish several results concerning common coupled fixed points and coupled coincidence points for mappings that fulfill various contractive conditions within the framework of complete C*-algebra valued rectangular parametric metric space. Furthermore,we demonstrate the applicability of these theorems by proving the existence and uniqueness of solution to a Fredholm nonlinear integral equation.