On some best proximity point results for multivalued mappings

This thesis is divided into four chapters. The first chapter discusses the motivation for the thesis and provides some background information on fixed point theory and best proximity point theory. In the second chapter, we recall the fundamentals definitions and notations, and some theorems related to our results about fixed point and best proximity point. We obtain our theorems in chapter three. The concepts of KW-type Ψ-contraction mapping inspired by the approaches of Wardowski and Klim-Wardowski have been presented. Then, we investigate the existence of a best proximity point for such mappings by considering a new family which is larger than the family of functions that is often used in fixed point results for multivalued mappings. Also, to demonstrate to effectiveness of our result we give a comparative example in which similar results in the literature cannot be applied. We provide our findings and suggestions in the fourth chapter.