Random approximations and fixed point theorems
This paper deals with stochastic versions of the best approximation theorem of \textit{K. Fan} [Math. Z. 112, 234-240 (1969; Zbl 0185.39503)] which states that for any \(E\)-valued continuous map defined on a compact, convex subset \(X\) of a normed space \(E\) there exists \(u\in X\) such that \(\text{dist}(f(u), X)= |u- f(u)|\). The authors obtain their random best approximation theorems for single valued and set-valued mappings by the use of random variational inequalities. Random fixed point theorems are then derived. The paper contains a rather comprehensive and useful reference list of 38 items.
stochastic versions of the best approximation theorem
scientific article; zbMATH DE number 847524