Approximations in random normed spaces (Q1386838)

The paper is concerned with best approximation in random normed spaces (random n.s.) [see \textit{G. Constantin} and \textit{I. Istrăţescu}, `Elements of probabilistic analysis with applications', Bucureşti (1989; Zbl 0694.60002)]. Completing some results obtained by \textit{A. N. Sherstnev}, Rev. Roum. Math. Pures Appl. 9, 771-789 (1964; Zbl 0132.38901)], the author defines the notion of uniformly convex random n.s, giving three equivalent conditions for uniform convexity, and proves that every closed convex set of a uniformly convex random n.s. is Chebyshevian.