Best Proximity Point Results via Simulation Functions in Metric-Like Spaces
01 Sep 2020-Kragujevac journal of mathematics (University Library in Kragujevac)-Vol. 44, Iss: 3, pp 401-413
TL;DR: In this paper, the existence of best proximity points of certain mappings via simulation functions in the frame of complete metric-like spaces is discussed and some consequences and examples are given.
Abstract: In this paper, we discuss the existence of best proximity points of certain mappings via simulation functions in the frame of complete metric-like spaces. Some consequences and examples are given of the obtained results.
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TL;DR: In this paper, the authors introduce a new concept of α - ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces.
Abstract: In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
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TL;DR: In this paper, the fixed point theory in metric-like spaces was initiated and some new fixed point results in partial metric spaces were derived, unifying and generalizing some well-known results in the literature.
Abstract: By a metric-like space, as a generalization of a partial metric space, we mean a pair , where X is a nonempty set and satisfies all of the conditions of a metric except that may be positive for . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our results unify and generalize some well-known results in the literature. MSC:47H10.
197 citations
"Best Proximity Point Results via Si..." refers background in this paper
...Among them, metric-like spaces, introduced by Amini-Harandi in [2], took a prominent place....
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TL;DR: In this paper, the authors introduce the notion of α-ψ-Meir-Keeler contractive mappings via a triangular α-admissible mapping, and discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces.
Abstract: In this paper, we introduce the notion of α-ψ-Meir-Keeler contractive mappings via a triangular α-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results.
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TL;DR: This paper slightly modify Khojasteh et?al.'s notion of simulation function and investigates the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions.
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TL;DR: In this paper, the existence and uniqueness of a fixed point of a cyclic mapping in the context of metric-like spaces is discussed, and some examples to illustrate the validity of the derived results are considered.
Abstract: In this paper, we notice the notions metric-like space and dislocated metric space are exactly the same. After this historical remark, we discuss the existence and uniqueness of a fixed point of a cyclic mapping in the context of metric-like spaces. We consider some examples to illustrate the validity of the derived results of this paper. MSC:47H10, 54H25.
71 citations