Disquisition on convergence, stability, and data dependence for a new fast iterative process

Abstract

This paper introduces a novel fast iterative process designed for approximating fixed points of contraction and weak contraction mappings. The study presents strong convergence results for this newly proposed iterative process, and proving its efficiency. Analytical and numerical evidences are provided to establish that the proposed iterative method converges more rapidly than several existing processes. Furthermore, stability results and dependence analysis are presented for the newly developed iterative process, enhancing its practical applicability and robustness.