For an arbitrary fixed segment [α, β] ⊂ R and given r ∈ N, A r , A 0, and p > 0, we solve the extremal problem
on the set of all functions x∈ L r ∞ such that ∥x (r)∥∞ ≤ A r and L(x) p ≤ A 0, where
In the case where p = ∞ and k ≥ 1, this problem was solved earlier by Bojanov and Naidenov.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 6, pp. 765 – 776, June, 2009.
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Kofanov, V.A. On some extremal problems of different metrics for differentiable functions on the axis. Ukr Math J 61, 908–922 (2009). https://doi.org/10.1007/s11253-009-0254-5
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DOI: https://doi.org/10.1007/s11253-009-0254-5