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https://dx.doi.org/10.1155/201...
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Approximate Best Proximity Pairs in Metric Space

Approximate best proximity pairs in metric space
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2011 English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,011 (issn: 1085-3375, eissn: 1687-0409, Copyright policy )
Authors: Mohsenalhosseini, S. A. M.; Mazaheri, H.; Dehghan, M. A.;

doi: 10.1155/2011/596971

Approximate Best Proximity Pairs in Metric Space

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.

Related Organizations
Keywords

Best approximation, Chebyshev systems, QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Top 10%
Average
gold