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On Best Proximity Point Theorems without Ordering

Author

Listed:
  • A. P. Farajzadeh
  • S. Plubtieng
  • K. Ungchittrakool

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:130439
DOI: 10.1155/2014/130439
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