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 (M_{C}) to improve and generalize (G_{C}). After that, present two concepts, proximal b-cyclic contraction type second type, on b-metric spaces. Then, obtain best proximity point results for such mappings in frameworks proximally complete spaces by using (M_{C}). Hence, some existing literature. Finally, illustrative interesting examples.