Approximate Best Proximity Pairs in Metric Space

الملخص EN

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.