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Best proximity point theorems on partially ordered sets

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Abstract

The main purpose of this article is to address a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. Indeed, if A and B are non-void subsets of a partially ordered set that is equipped with a metric, and S is a non-self mapping from A to B, this paper scrutinizes the existence of an optimal approximate solution, called a best proximity point of the mapping S, to the operator equation Sx = x where S is a continuous, proximally monotone, ordered proximal contraction. Further, this paper manifests an iterative algorithm for discovering such an optimal approximate solution. As a special case of the result obtained in this article, an interesting fixed point theorem on partially ordered sets is deduced.

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  1. Department of Mathematics, Anna University, Chennai, 600 025, India

    S. Sadiq Basha

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  1. S. Sadiq Basha
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Correspondence to S. Sadiq Basha.

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Basha, S.S. Best proximity point theorems on partially ordered sets. Optim Lett 7, 1035–1043 (2013). https://doi.org/10.1007/s11590-012-0489-1

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