Aslantaş, Mustafa2021-11-302021-11-302021-06-30https://doi.org/10.31801/cfsuasmas.780729http://hdl.handle.net/20.500.12575/76497In this paper, we first introduce a new notion of the property (M_{C}) to improve and generalize the property (G_{C}). After that, we present two new concepts, proximal b-cyclic contraction of first type and second type, on b-metric spaces. Then, we obtain two best proximity point results for such mappings in the frameworks of best proximally complete b-metric spaces by using the property (M_{C}). Hence, we generalize some results existing in the literature. Finally, we present some illustrative and interesting examples.enBest proximity pointProximal b-cyclic contractionb-metric spaceArticle7014834962618-6470