Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces
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Date
2021-06-30
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Ankara Üniversitesi Fen Fakültesi
Abstract
In 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.
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Best proximity point, Proximal b-cyclic contraction, b-metric space