Some best proximity point results on partial metric spaces

This thesis consists of five chapters. In the first chapter, we give basic definitions and theorems that will be used throughout the thesis are given. In the second chapter, we introduce new concepts of BG-contraction mapping and proximal BG-contraction mapping. Then, we obtain some best proximity point results. Hence, we generalize and improve results existing in the literature. Also, we provide nontrivial example to show the effect of our result. In the third chapter, we introduce a concept of Fp-contraction mapping. Then, we obtain a best proximity point for such mappings. Hence, we extend and generalize some results existing in the literature. Also, we provide an example to demonstrate the effectiveness of our result. In the fourth chapter, we give an existence and uniqueness result for solution of nonlinear Freldhom and Volterra integral aligns. In the last section, discussion and recommadation are given.