Some fixed point theorems in graphical metric spaces

In this study, informations about partial order relation and graph theory are given and some fixed point theorems in graph metric spaces are examined. Firstly, the basic definitions and theorems to be used throughout the thesis are given. Then, by giving graphical metric space, some topological properties on such space are examined. Subsequently, some generalizations of Banach's fixed point theorem in graphical metric space are proved. In the next section, by examining graphical b-metric space and some topological properties of such space, the fixed point theorems in graphical metric spaces are moved to graphical b-metric spaces. In addition, some examples are given to demonstrate the effectiveness of the main theorems. Finally, the notion of graphical extended b-metric space is introduced and some fixed point theorems on this space are investigated.