هندسه متري Έو نظريه بهترين تقريب

Metric Geometry an‎d Best Approximation Theory

رياضي

This dissertation investigates metric geometry an‎d the extension of fixed-point theorems within the framework of geodesic metric spaces, with a particular emphasis on Busemann convex an‎d CAT(0) spaces. The first chapter introduces the fundamentals of metric geometry, encompassing length spaces, geodesics, an‎d various types of convexity. The second chapter, focusing on best approximation theory, examines the geometric properties of pairs of sets an‎d concepts such as the UC property an‎d proximal normal structure (PNS). The third chapter is dedicated to the study of relatively Jaggi nonexpansive mappings (both cyclic an‎d noncyclic) as well as relatively u-continuous mappings, generalizing fundamental theorems including Fanʹs best approximation theorem an‎d the Markov-Kakutani theorem. In the fourth chapter, cyclic p-contraction an‎d p-nonexpansive mappings are analyzed, an‎d Ulam-Hyers stability for coupled best proximity points problems is established. Finally, the fifth chapter generalizes three classical theorems of functional analysis—namely, Kirkʹs fixed point theorem, Kirk an‎d Royaltyʹs fixed point theorem, an‎d the Goebel-Karlovitz lemma—within the comprehensive setting of reflexive Busemann convex spaces. The principal contribution of this thesis lies in the expansion of fixed-point an‎d best approximation theory beyond linear spaces an‎d the introduction of a geometric framework for analyzing existential problems in abstract metric spaces.

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موسي گابله

157736