Fixed point theorems on some metric spaces

This thesis consists of six chapters. In the first chapter, the subject of the thesis is introduced, in the second chapter, in order to make the understanding easy, some basic notions about soft sets and metric spaces are given. In the third chapter, the concept of a partial b-metric space, which is an generalization of b-metric space, is presented and investigated how a topological space is derived from this metric space. Then, convergence properties on this metric space are studied and some fixed point theorems are established. In the fourth chapter, generalized b-metric space is defined and its relation with b-metric space is investigated. Also, fixed point theorems are studied on this space and supported with examples. In the fifth section, by using soft set theory, soft metric space is defined and a soft topological space is obtained from this space. Next, basic concepts such as soft convergence and soft Cauchy sequence are given on soft metric spaces and their important properties are investigated. In the last chapter, a soft topology is introduced with regard to a soft mapping and some basic properties of this soft topology are studied. Also, the concept of a soft orbit is presented and supported with examples. Moreover, the concept of a soft b-metric space is given, which is a soft version of b-metric spaces. Finally, by using these concepts, some fixed point theorems are proved.