The best uniform approximation in the metric space of continuous maps with compact convex images - Hnatyuk, Yu. V. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
For the problem of the best uniform approximation of a continuous map with compact convex images by sets of other continuous maps with compact convex images, we establish necessary and sufficient conditions and the criterion for an extremal element, which is a generalization of the classical Kolmogorov criterion for the polynomial of best approximation.