We solve an extremal problem
in a class of pairs (x, I) of functions \(x \in {S}_{\varphi }^{k}\) such that \({\varphi }^{\left(i\right)}\) are the comparison functions for \({x}^{\left(i\right)},\) i = 0, 1,…,k, and the intervals I = [a, b] satisfy the conditions
where
In particular, we solve the same problems on the classes \({W}_{\infty }^{r}\left(\mathbf{R}\right)\) and on bounded sets of spaces of trigonometric polynomials and splines, as well as the Erdős problem for the positive (negative) parts of polynomials and splines.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 2, pp. 182–197, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.7259.
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Kofanov, V. Bojanov–Naidenov Problem for Differentiable Functions and the Erdős Problem for Polynomials and Splines. Ukr Math J 75, 206–224 (2023). https://doi.org/10.1007/s11253-023-02194-7
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DOI: https://doi.org/10.1007/s11253-023-02194-7