The aim of this paper is to present a novel stationary and nonstationary iterative approach for approximating common fixed points of a finite family of generalized nonexpansive mappings in uniformly convex Banach spaces. For the stationary scheme, both strong and weak convergence theorems are established under standard geometric conditions. Addressing an open problem, that is, “under what conditions nonstationary algorithm converge to a common fixed point of the generalized nonexpansive mapping,” thus we propose a nonstationary iterative method that dynamically adapts to varying parameters, and we derive sufficient conditions for its convergence. The asymptotic regularity and stability of the nonstationary method are rigorously analyzed. A comprehensive numerical example, supported by MATLAB simulations, demonstrates the practical convergence behavior of the proposed schemes and validates the theoretical findings. These results contribute to the growing body of fixed point theory and offer potential applications in areas such as signal processing, image reconstruction, and machine learning. MSC2020 Classification 47H10, 47J26, 47H09, 46B06
Afsheen et al. (Thu,) studied this question.