Approximate Best Proximity Pairs in Metric Space

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

Abstract and Applied Analysis, 2011, vol. 2011, 1-9

Abstract:

Let ð ´ and ð µ be nonempty subsets of a metric space ð ‘‹ and also 𠑇 ∶ ð ´ âˆª ð µ â†’ ð ´ âˆª ð µ and 𠑇 ( ð ´ ) ⊆ ð µ , 𠑇 ( ð µ ) ⊆ ð ´ . We are going to consider element ð ‘¥ ∈ ð ´ such that ð ‘‘ ( ð ‘¥ , 𠑇 ð ‘¥ ) ≤ ð ‘‘ ( ð ´ , ð µ ) + 𠜖 for some 𠜖 > 0 . We call pair ( ð ´ , ð µ ) an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, 𠑇 -minimizing a sequence are given in a metric space.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:596971

DOI: 10.1155/2011/596971

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