Extremal problems of approximation theory in fuzzy contact (Q1304276)

Let \(X\) be a normed space, \(U,V\subseteq X\) and \(x\in X\). The classical best approximation problem is to determine \(E(x,U):=\inf_{x\in U}\|x-u\|\) and \(E(V,U): =\sup_{x\in V} E(x,U)\). The authors generalize these problems to fuzzy sets \(V\) and apply their theory to certain Lebesgue spaces \(L^p_r\) of differentiable functions. This continues their programme begun in Acta Univ. Latviensis 606, 9-18 (1997).