A better iterative algorithm for fixed-point problem in Banach spaces with application

In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings.