Convergence analysis of Suzuki's generalized nonexpansive mappings using the Picard-Abbas iteration process.

Abstract

This manuscript investigates the convergence behavior of Suzuki's generalized nonexpansive mappings using the recently introduced Picard-Abbas iteration process. We establish both weak and strong convergence results for the associated fixed-point approximations. To demonstrate the effectiveness of our approach, a numerical example is provided. Furthermore, we generate polynomiographs based on the proposed iteration process and compare them with those produced by existing methods, highlighting the advantages and visual insights offered by our scheme.