### Inequalities of various metrics for the norms $$$\|x\|_{p,\delta} = \sup \bigl\{ \| x \|_{L_p[a,b]} \colon a,b\in \mathbb{R}, b-a\leqslant \delta \bigr\}$$$ of differentiable functions on the real domain

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Kofanov V.A. "Inequalities of various metrics for differentiable periodic functions", *Ukrainian Math. J.*, 2015; 67(2): pp. 202-212. (in Russian)

Pinkus A., Shisha O. "Variations on the Chebyshev and $$$L^q$$$-Theories of Best Approximation", *Journal of Approx. Theory*, 1982; 35(2): pp. 148-168.

Kofanov V.A. "Solution of Bojanov-Naidenov problem with constraints for the norm $$$\|\cdot \|_{p,\delta}$$$", *Dnipr. Univ. Math. Bull.*, 2017; 22: pp. 41-50. (in Russian)

Korneichuk N.P., Babenko V.F., Ligun A.A. *Extremum properties of polynomials and splines*, Naukova dumka, Kyiv, 1992. (in Russian)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", *Izbr. tr. Matematika, mekhanika*, Nauka, Moscow, 1985; pp. 252-263. (in Russian)

Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. *Inequalities for derivatives and their applications*, Nauk. dumka, Kyiv, 2003; 590 p. (in Russian)

Levitan B.M. *Almost periodic functions*, Moscow, 1953; 396 p. (in Russian)

Weyl H. "Almost periodic invariant vector sets in a metric vector spase", *Amer. Journ. of Math.*, 1949; 71(1): pp. 178-205.

Babenko V.F., Selivanova S.A. "On inequalities of Kolmogorov type for periodic and non-periodic functions", *Differential equations and their applications*, Dnipropetrovsk, Dnipropetrovsk Nat. Univ., 1998; pp. 91-95. (in Russian)

Kofanov V.A. "Some extremal problems in various metrics and sharp inequalities of Nagy-Kolmogorov type", * East. J. Approx.*, 2010; 16(4): p. 313-334.

Kofanov V.A. "Inequalities for non-periodic splines and their derivatives on the real domain", *Ukrainian Math. J.*, 2014; 66(2): pp. 216-225. (in Russian)

DOI: https://dx.doi.org/10.15421/241806

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