Some fixed point theorems in non-complete metric spaces

In this thesis, some fixed point theorems in non-complete metric spaces are investigated. This study consists of three chapters. The first chapter is the introduction part and the preliminary informations about this work is given. In the second chapter, under the title of material and method, basic concepts related to the subject are given. Then fixed point concept and Banach contraction principle, fixed point theorems in α-complete metric spaces and fixed point theorems for generalized w_α-set-valued contraction mappings in α-complete metric spaces are investigated. In the third chapter, research and findings, fixed point results on R-relation sets by w-distance method are examined. Then the definitions of w-α-distance and the generalized w-α-rational contraction mapping, related theorem and example are given. Also, w-α-rational contraction mapping is defined and by using this definition, the theorem related fixed point is expressed and proved. The part of discussion and conclusion that is final chapter, the results obtained here in interpreted and it is emphasized that some fixed point theorems exist in the literature.