In this paper, we introduce the notion of (S) convex structure, thereby, we acquire a best proximity point theorem for tricyclic contractions in the framework of convex metric spaces.Mathematics Subject Classification: 47H09, 47H10, 54H25
We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial S b -metric spaces. In this way, we obtain extensions of some results in the literature.
In this note, we present a best proximity point theorem for tricyclic contractions in the setting of CAT(0) spaces. In the same context, we give an elaborate counterexample.
This paper introduces a new class of mappings called
S
-Geraphty-contractions and provides sufficient conditions for the existence and uniqueness of a best proximity point for such mappings. It also presents the best proximity point result for generalized contractions as well. Our results extend and generalize some theorems in the literature.
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