Exploring the existence of a solution of nonlinear Fredholm integral equations: Novel approaches to estimating common fixed points

This study explores common fixed points for mappings that satisfy the non-symmetric Garcia-Falset property in a Banach space with uniform convexity and a digraph G. By leveraging coordinate convexity, we analyze the convergence outcomes of the modified AA -iterative algorithm. We aim to identify common fixed points through a series of convergence analyses and offer an illustrative example to validate our findings for such mappings. Utilizing these common fixed point results in conjunction with illustrative examples, we establish the existence of a common solution to a system of nonlinear Fredholm integral equations. This research presents novel approaches for addressing nonlinear Fredholm integral equations by investigating the estimation of common fixed points, showcasing these methodologies’ potential applications and implications in solving complex mathematical problems.