### Extremal problems for non-periodic splines on real domain and their derivatives

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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)

Babenko V.F. "Researches of Dnipropetrovsk mathematicians on inequalities for derivatives of periodic functions and their applications", *Ukrainian Math. J.*, 2000, 52(1): pp. 5-29. (in Russian)

Kwong M.K., Zettl A. "Norm inequalities for derivatives and differences", *Lecture notes in mathematics*, Berlin: Springer-Verlag, 1992; 1536: 150 p.

Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", *J. d'Analyse Mathematique*, 1999; 78: pp. 263-280.

Erdös P. "Open problems", *Open Problems in Approximation Theory* (B. Bojanov, ed.), SCT Publishing, Singapur, 1994; pp. 238-242.

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. "Some extremum problems in different metrics for differentiable functions on the real domain", *Ukrainian Math. J.*, 2009; 61(6): pp. 765-776. (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. "Exact upper bounds of norms of functions and their derivatives on the classes of functions with given comparison function", *Ukrainian Math. J.*, 2011; 63(7): pp. 969-984. (in Russian)

Kofanov V.A. "Bojanov-Naidenov problem for differentiable functions on the axis and inequalities of various metrics", *Ukrainian Math. J.*, 2019; 71(6): pp. 786-800. (in Russian)

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

Magaril-Il'yaev G.G. "On the best approximation of functional classes by splines on the real domain", *Trudy Matematicheskogo instituta RAN*, 1992; 194: pp. 148-159. (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., Ligun A.A. *Extremum properties of polynomials and splines*, Naukova dumka, Kyiv, 1992. (in Russian)

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/10.15421/241903

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