Nonstandart methods in fixed point theory

11 ABSTRACT Master of Science Thesis NONSTANDART METHODS in FIXED POINT THEORY EMRAH AKYAR Anadolu University- Graduate School of Natural And Applied Sciences Mathematics Program Supervisor: Prof. Orhan ÖZER 1998, Page 62 This thesis is an exposition on the work done in recent years about the existence of nonexpansive mappings and about some results took place in various literature given with nonstandard proof. This work consists of three chapters. In the first chapter, in order to aim ultraproduct techniques some preparations are done and some important theorems are given. In the second chapter, the fixed point theory in general is considered and its relation with some geometric properties are given. In the last chapter, some fixed point theorems which are obtained by ultraproduct techniques are given and some important theorems of Maurey, who is the pioneer of theory, are listed. Keywords: Nonexpansive Mappings, Fixed Point Property, Ultra Products