In this paper we obtain some best proximity point results using almost contractive condition with three control functions (in which two of them need not be continuous) in partially ordered metric spaces. As an application, we prove coupled best proximity theorems. The results presented in this paper generalize the results of Choudhury, Metiya, Postolache and Konar [8]. We draw several corollaries and give illustrative examples to demonstrate the validity of our results.
The primary goal of this research is to derive generalized C_G-class functions and prove that a fixed point exists for α-F_G (ξ,λ,θ)-generalized Suzuki contraction on b_v (s) -metric spaces. In our study, we use some properties of different control functions. Our findings broaden and unify a number of previous results in the literature. The conclusions are supported by examples.
HIGHLIGHTS
This paper focuses on defining the C_G-Class Functions
α-F_G (ξ,λ,θ)-generalized Suzuki contractions in b_v (s)-Metric Spaces is proposed and a result is proved
Examples are provided for α-F_G (ξ,λ,θ)-generalized Suzuki contractions, C_G-class function, and b_v (s)-metric spaces
In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and provethe existence and uniqueness of xed points in complete S-metric spaces. We alsoprove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.
In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.
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