Abstract
We introduce a type of Geraghty contractions in aJS-metric spaceX,calledα,D-proximal generalized Geraghty mappings. By using the triangular-α,D-proximal admissible property, we obtain the existence and uniqueness theorem of best proximity coincidence points for these mappings together with some corollaries and illustrative examples. As an application, we give a best proximity coincidence point result inXendowed with a binary relation.
Highlights
Introduction and PreliminariesThe concept of the best proximity coincidence point, which is an extension of a best proximity point problem, was mentioned in [21] (see [22]) where some results of mappings in generalized metric spaces were presented
Introduction and PreliminariesLet T : A → B be a map where A and B are two nonempty subsets of a metric space X: It is known that if T is a nonself-map, the equation Tx = x does not always have a solution, and it clearly has no solution when A and B are disjoint
We introduce a type of Geraghty contractions which will be called ðα, DÞ-proximal generalized Geraghty mappings
Summary
The concept of the best proximity coincidence point, which is an extension of a best proximity point problem, was mentioned in [21] (see [22]) where some results of mappings in generalized metric spaces were presented. In general, results of best proximity points using the weak P -property in usual metric spaces might not be attained in the setting of JS -metric spaces. We introduce a type of Geraghty contractions which will be called ðα, DÞ-proximal generalized Geraghty mappings. These maps are motivated by the work of Khemphet [37]. Using the weak P-property in the setting of JS-metric space, we establish a result on the existence and uniqueness of the best proximity coincidence point for these mappings. Note that some other results of best proximity points in X endowed with binary relations can be deduced from our result
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