On Best Proximity Point Theorems without Ordering

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

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 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 Sx = 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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:130439

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