Abstract
The primary objective of this paper is the study of the generalization of some results given by Basha (Numer. Funct. Anal. Optim. 31:569–576, 2010). We present a new theorem on the existence and uniqueness of best proximity points for proximal β-quasi-contractive mappings for non-self-mappings S:Mrightarrow N and T:Nrightarrow M. Furthermore, as a consequence, we give a new result on the existence and uniqueness of a common fixed point of two self mappings.
Highlights
In 1969, Fan in [2] proposed the concept best proximity point result for non-self continuous mappings T : A −→ X where A is a non-empty compact convex subset of a Hausdorff locally convex topological vector space X
In 2010, [1], Basha introduce the concept of best proximity point of a non-self mapping
He introduced an extension of the Banach contraction principle by a best proximity theorem
Summary
In 1969, Fan in [2] proposed the concept best proximity point result for non-self continuous mappings T : A −→ X where A is a non-empty compact convex subset of a Hausdorff locally convex topological vector space X. He showed that there exists a such that d(a, Ta) = d(Ta, A). In 2010, [1], Basha introduce the concept of best proximity point of a non-self mapping He introduced an extension of the Banach contraction principle by a best proximity theorem. Best proximity point theorems for non-self set valued mappings have been obtained in [20] by Jleli and Samet, in the context of proximal orbital completeness condition which is weaker than the compactness condition
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