BEST PROXIMITY POINT THEOREMS FOR PROXIMAL b-CYCLIC CONTRACTIONS ON b-METRIC SPACES.

In this paper, we first introduce a new notion of the property (MC) to improve and generalize the property (GC). After that, we present two new concepts, proximal b-cyclic contraction of the first type and second type, on b-metric spaces. Then, we obtain two best proximity point theorems for such mappings in the framework of best proximally complete b-metric spaces by using the property (MC). Hence, we generalize some results existing in the literature. Finally, we present some illustrative and interesting examples. [ABSTRACT FROM AUTHOR]