Exploring Fixed Point Theory in Quasi-Partial Metric Spaces: A Unified Approach with Applications in Integral Equations and Computational Sciences

Abstract

This paper explores the concept of $\mathcal{C}$-class functions, which encompass a wide range of contractive conditions and applies them to derive common fixed-point results for two pairs of self-mappings in quasi-partial metric spaces. These findings extend existing theories by introducing generalized contractive conditions and providing a broader framework for fixed-point analysis. A detailed example is constructed to validate the results, illustrating the practical application of the established theorems. Furthermore, the paper demonstrates the relevance of these results by applying them to solve a system of integral equations diffusion reaction, highlighting their utility in addressing real-world mathematical problems.