Effectiveness of Picard–Abbas iteration for fixed point approximation of mappings satisfying condition (E)

Abstract

In this paper, we investigate the convergence properties of mappings that satisfy condition ($E$) by employing the recently introduced Picard–Abbas iteration process. We establish both weak and strong fixed-point convergence results for these mappings. To validate our findings, we provide a novel numerical example. Furthermore, we generate polynomiographs using the proposed iteration process and compare them with those obtained from other methods. This comparison highlights the effectiveness and potential advantages of our approach.