Fiksne i najbolje aproksimacije tačke za preslikavanja na metričkim prostorima i uopštenjima

Abstract

The theme of this doctoral dissertation are best proximity point and fixed point theorems for operators on metric and generalized metric spaces. From the corresponding best proximity point theorems, it is possible to derive as consequences, the statements about fixed points for given type of mappings. Similarly, from the results in spaces with a generalized metrics, we further deduce corresponding results on usual metric spaces. In that manner, some well-known results of fixed point theory are unified. The text of the dissertation is divided into three chapters. The first chapter is of introductory character. The second chapter contains the main results which were obtained by the author independently or in co-authorship in papers published in distinguished international journals on the SCI list. In the third chapter, the applications of the main results to integral equations and variational inequalities are studied, and some directions for further research are outlined.