On fixed point teorems

This thesis consists of five chapters. In the first chapter, the subject of the thesis is introduced, in the second chapter, with aim of making easier, basic concepts related to metric spaces and fixed point theory are given. In the third chapter, the concept of a complex valued metric space is expressed and the fixed point theorems are established for mappings satisfying some contractive conditions on this space. Also, these theorems are supported with examples. In the fourth chapter, the concept of a complex valued b-metric space, which is a generalization of complex valued metric space, is presented and various fixed point theorems are investigated. Finally, some new fixed point theorems are proved on complex valued b-metric space.