Some best proximity point results for multivalued F-contractions on quasi metric space

This thesis is divided into four parts. The first part gives the motivation of the thesis and some background information on fixed point theory and best proximity point theory. In the second part, we recall the basic definitions, notations, and some theorems regarding the fixed point and the best proximity point. We present our results in the third section. We first introduce the concept of the Suzuki type F_(α,d) contraction mapping inspired by the approaches of Wardowski and Suzuki. Next, we investigate the existence of the best convergence point for such mappings by considering a new family larger than the family of functions often used in fixed-point results for these transformations. We also give a comparative example where similar results in the literature cannot be applied to demonstrate the effectiveness of our results. We present our findings and recommendations in the fourth section.