Geometry in metric spaces and fixed point theorems for classes of nonexpansive type mappings

Abstract

The main purpose of this work is to present recent results obtained on the existence of Fxed points for nonexpansive mappings and orbit-nonexpansive mappings in the general context of metric spaces. Additionally, our tech- niques will allow us to deduce the existence of common xed points for groups of such mappings based on features of the closed balls of the metric space. In order to do that, the concepts of normal structure and uniform normal structure will be analyzed and extended from the Banach space framework to the more general environment of metric spaces. Applications to important families of metric spaces without linear structure will be dis- played. The work is divided into three chapters which are subdivided into sec- tions. In Chapter 1 we present the basic concepts and results that we believe are necessary for reading and understanding the other chapters. In Chapter 2 and Chapter 3 we present the aforemetioned results most of which can be found in the articles [1] and [2] by Rafael Espínola García, María Japón and myself.