For the problem of the best uniform approximation of a continuous mapping with compact convex images by sets of other continuous mappings with compact convex images, we establish necessary and sufficient conditions and a criterion for an element to be extremal; the criterion obtained is a generalization of the classic Kolmogorov criterion for a polynomial of the best approximation.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1620–1633, December, 2010.
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Hnatyuk, Y.V. Best uniform approximation in the metric space of continuous mappings with compact convex images. Ukr Math J 62, 1879–1895 (2011). https://doi.org/10.1007/s11253-011-0477-0
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DOI: https://doi.org/10.1007/s11253-011-0477-0