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2014 On Best Proximity Point Theorems without Ordering
A. P. Farajzadeh, S. Plubtieng, K. Ungchittrakool
Abstr. Appl. Anal. 2014(SI49): 1-5 (2014). DOI: 10.1155/2014/130439


Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if A and B are nonvoid subsets of a partially ordered set that is equipped with a metric and S is a non-self-mapping from A to B , then the mapping S has an optimal approximate solution, called a best proximity point of the mapping S , to the operator equation S x = x , when S is a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on S .


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A. P. Farajzadeh. S. Plubtieng. K. Ungchittrakool. "On Best Proximity Point Theorems without Ordering." Abstr. Appl. Anal. 2014 (SI49) 1 - 5, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07021767
MathSciNet: MR3166563
Digital Object Identifier: 10.1155/2014/130439

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI49 • 2014
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