On the generalization of metric, ultrametric and ordered fixed point theorems

This thesis aims to study a generalization of Banach Fixed Point Theorem in metric, ultrametric and ordered spaces following a recent paper of Kuhlmann and Kuhlmann (2015) which points out the common denominator of Banach's Fixed Point Theorem in metric, ultrametric and topological spaces. The general idea is to give a general fixed point theorem which works in all of these spaces by the structure of ball spaces and by the concept of spherical completeness. This thesis includes six chapters. Chapter 1 introduces the literature and the objective of this thesis. Chapter 2 gives the preliminaries. In Chapter 3, Banach Fixed Point Theorem is given. In Chapter 4, we study the ultrametric spaces. Some examples including the remarkable p-adic spaces are given. Chapter 5 presents the ordered spaces and some fixed point theorems in these spaces. In Chapter 6, we give the general fixed point theorem due to Kuhlmann and Kuhlmann (2015) which combines various contents. Finally, we conclude with the proofs of Banach fixed point theorem, ultrametric fixed point theorem and as a our contribution to literature Bourbaki and Witt theorems given in ordered spaces by applying the general fixed point theorem.