In this paper, we introduce the notions of S-proximal Berinde g-cyclic contraction two nonself mappings and g-contractions first kind second in an S-metric space prove some coincidence best proximity point theorems for these types space. Also, give examples to analyze support our main results. The results presented here generalize existing literature.

in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wedene the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...