Some results on existence and convergence of best proximity points (Q2837854)
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scientific article; zbMATH DE number 6184860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on existence and convergence of best proximity points |
scientific article; zbMATH DE number 6184860 |
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8 July 2013
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metric space
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uniformly convex Banach space
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generalized cyclic contraction
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best proximity point
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strict convexity
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Some results on existence and convergence of best proximity points (English)
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Let \(A\) and \(B\) be nonempty subsets of a metric space \((X,d)\) and \(T: A \cup B \to A \cup B \) a generalized cyclic contraction. The authors prove some theorems that generalize some results of \textit{A. A. Eldred} and \textit{P. Veeramani} [J. Math. Anal. Appl. 323, No. 2, 1001--1006 (2006; Zbl 1105.54021)] and of \textit{M. A. Al-Thagafi} and \textit{N. Shahzad} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 10, 3665--3671 (2009; Zbl 1197.47067)].
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