On a novel semigroup of enriched Chatterjea-type mappings in Banach spaces with a numerical experiment

Recently in [V. Berinde and M. Păcurar, Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces, J. Fixed Point Theory Appl., 23(4):66, 2021], using the technique of enrichment of contractive mappings by Krasnoselskij averaging, Berinde and Păcurar introduced a new type of mappings, called enriched Chatterjea-type mappings. The main aim of this article is to introduce a new semigroup of enriched Chatterjea-type mappings. We also establish weak and strong convergence results for enriched Chatterjea-type semigroups using a novel iterative process in uniformly convex Banach spaces. To support the theoretical results, we conduct numerical experiments demonstrating the convergence behavior of the iterative scheme under various initial conditions and control sequences. The findings confirm exponential convergence and highlight the effectiveness and robustness of the proposed method for common fixed point approximation.