Approximate Best Proximity Pairs in Metric Space | Zendy

S. A. M. Mohsenalhosseini | Zendy; H. Mazaheri | Zendy; M. A. Dehghan | Zendy

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Approximate Best Proximity Pairs in Metric Space

Author(s) -

S. A. M. Mohsenalhosseini,

H. Mazaheri,

M. A. Dehghan

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/596971

Subject(s) - mathematics , metric space , metric (unit) , space (punctuation) , combinatorics , pure mathematics , mathematical analysis , computer science , operations management , economics , operating system

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

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