Pseudocontractive Mappings: A Review of New Iteration Processes and Convergence Results

Abstract : Pseudocontractive mappings are a fundamental concept in nonlinear analysis, with wide-ranging applications in optimization, differential equations, and control theory. This review provides a comprehensive overview of recent iteration processes for approximating fixed points of pseudocontractive mappings, highlighting theoretical advancements, convergence results, and numerical implementations. Various iterative schemes are examined in terms of their mathematical foundations, convergence properties, and computational effectiveness. The paper consolidates the existing literature, identifies open research problems, and outlines potential directions for future investigations.