On Best Proximity Point Theorems without Ordering

A. P. Farajzadeh, S. Plubtieng and K. Ungchittrakool

Abstract and Applied Analysis, 2014, vol. 2014, 1-5

Abstract:

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 and are nonvoid subsets of a partially ordered set that is equipped with a metric and is a non-self-mapping from to , then the mapping has an optimal approximate solution, called a best proximity point of the mapping , to the operator equation , when 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 .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:130439

DOI: 10.1155/2014/130439

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