A Comparative Analysis of Classical Contractive Mappings: Sharp Constants, Inclusion Conditions, and Picard Iteration Performance - Syamsuddin Mas'ud (University of Mataram, 2026)
There are some of the classical contractive mappings introduced by Banach, Kannan, Chatterjea, Reich, Hardy–Rogers, and Ćirić. They remain fundamental in fixed point theory. While their theoretical properties are well documented, a detailed and systematic comparison of the convergence performance of Picard iterations among these classes is still lacking in the literature. This study presents a comparative analysis from a numerical perspective on a complete metric space. We check the sharp constants of their contractions, inclusion relationships, establish a sufficient condition for a Chatterjea contraction to be a Reich contraction, and evaluate the practical performance of Picard iteration through simple numerical experiments. We give two concrete examples, a linear map and a quadratic polynomial for this numerical experiment. They are provided to show that the intersection of all six classical classes is not limited to linear mappings. A hierarchical diagram and structural comparison table are also given to support our study. The integration of theoretical results and numerical validation offers a clearer and more practical reference for students and researchers in studying the concepts of fixed point theory.