Some coincidence best proximity point results in S-metric spaces

In this thesis study, the coincidence best proximity point theorems obtained for the proximal Berinde g-contraction mappings of the first kind and second kind and the proximal Berinde g-cyclic contraction of two nonself mappings in metric spaces are generalized to S-metric spaces. This thesis consists of five sections. Firstly, introductory section which it is introduced of problem in thesis is given. Afterwards, basic definitions and concepts, which are used in the study, are given in the second section, named as 'Basic Concepts'. In the third section, firstly, the definitions of best proximity point and coincidence best proximity point are given. Later, the proximal cyclic mappings are discussed and the proximal Berinde g-contraction mappings of the first kind and second kind are examined. Finally, the definition of the S-metric space and some basic topological concepts in this space are given. In the fourth section, the S-proximal Berinde g-cyclic contraction of two nonself mappings and the S-proximal Berinde g-contraction mappings of the first kind and second kind in S-metric spaces are introduced. Later, some coincidence best proximity theorems are proved for these kinds of nonself mapping in this space. In addition, two examples are presented to support the results. In the last section, the results and remarks, obtained in the study are included. Keywords: S-metric space, Best proximity point, Coincidence best proximity point, S-proximal Berinde g-cyclic contraction