Innovative Method for Proving Iterative Convergence of Strictly Nonexpansive Operators in Bounded Domains

Abstract: This paper makes substantial theoretical advancements in fixed point theory for strictly nonexpansive mappings. By developing an innovative proof technique, we successfully generalize the classical fixed-point theorem for strictly nonexpansive mappings originally established for compact sets to broader cases involving bounded sets. The key innovations lie in leveraging both the boundedness property of iterative sequences and the strict nonexpansiveness of mappings, which collectively enable us to significantly relax the conventional requirements of spatial convexity and compactness typically imposed on general nonexpansive mappings.