Best proximity pair theorems for a family of sets (Q2782471)

In the case when the fixed point equation \(Tx=x\), where \(T\) is a non-self operator, does not have a solution, then the next attempt is to find an element in a suitable space such that \(x\) is close to \(Tx\) in some sense. Such best approximation theorems are due to Ky Fan, Reich, Segal and others. In the present paper best proximity pair theorems furnishing sufficient conditions for the existence of an element \(x_0\) in a non-empty compact convex subset \(A\) such that \(a(x_0,T_i(x_0)) =d(A,B_i)\), \(i=1,\dots,n\), are proved for given non-empty subsets \(A\), \(B_i\), \(i=1, \dots,n\) of a normed linear space \(E\) and \(n\) Kakutani factorizable multifunctions \(T_i:A\to 2^{B_i}\), \(i=1, \dots,n\).NEWLINENEWLINEFor the entire collection see [Zbl 0980.00021].