Approximate Best Proximity Pairs in Metric Space

S. A. M. Mohsenalhosseini, H. Mazaheri and M. A. Dehghan

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: Let A and B be nonempty subsets of a metric space X and also T : A ∪ B → A ∪ B and T(A)⊆B, T(B)⊆A. We are going to consider element x ∈ A such that d(x, Tx) ≤ d(A, B) + ϵ for some ϵ > 0. We call pair (A, B) an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, T‐minimizing a sequence are given in a metric space.

Date: 2011
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https://doi.org/10.1155/2011/596971

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:596971

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