Metric areas and results of best periodic points.

This thesis consists of four parts. In the first chapter, the basic definitions and theorems that will be used throughout the thesis are given. In the second part, we obtain some of the best periodic proximity point results in metric spaces for p-contraction type mappings. Thus, we generalize and improve the similar results existing in the literature. In the third section, we demonstrate some of the best periodic proximity point results in metric spaces for nonunique contraction mappings. Some generalizations of both the fixed point and best proximity point results have been obtained for nonunique contraction mappings. [ABSTRACT FROM AUTHOR]