Convergence Behavior of the F ∗ Algorithm: Strong and Weak Results for Nonexpansive Mappings

This study examines the strong and weak convergence of the F ∗ iterative approach to the fixed point of a nonexpansive mapping in the context of a Banach space. This work shows improved rate and efficiency of convergence. Furthermore, we proved that F ∗ iterative algorithm converges to a fixed point faster than Picard, Mann, S, and Varat iterative algorithms. Finally, we provide numerical examples to support the main results and provide numerical and graphical representations through MATLAB.