Orthogonal quasi metric spaces

In this thesis study, firstly orthogonal metric space and quasi metric space structures were considered together and orthogonal quasi metric space structure was obtained. Afterwards, the existence and uniqueness of fixed points were examined when some appropriate contraction conditions were met for the self mappings defined on this structure. The study consists of four chapters. In the first chapter, a summary of the literature on orthogonal spaces and fixed point theorems is given. In the second section, the preliminaries, definitions and theorems necessary for this study are mentioned. In the third section, we discuss the fixed point theorems and caveats we obtained for the newly defined orthogonal quasi metric spaces and their application to Volterra-integral equations with the help of weak contraction. In the last section we summarize all our results.