Bernstein type inequalities of different metrics for splines defined on the real domain

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), http://orcid.org/0000-0001-6677-1914
V.A. Zontov (Oles Honchar Dnipropetrovsk National University)

Abstract


New sharp Bernstein type inequalities of different metrics in spaces of integrable functions for non-periodic splines of order m and minimal defect, having equidistant nodes, are obtained.

Keywords


non-periodic splines; Bernstein type inequalities of different metrics

References


Korneichuk N.P. Exact constants in approximation theory, Nauka, Moscow, 1987. (in Russian)

Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi mat. nauk, 1960; 15(3): pp. 81-120. (in Russian)

Subbotin Yu.N. "On the piecewise-polynomial interpolation", Mat. zametki, 1967; 1(1): pp. 24-29. (in Russian)

Babenko V.F., Pichugov S.A. "Bernstein type inequalities for polynomial splines in $$$L_2$$$ space", Ukrainian Math. J., 1991; 43(3): pp. 420-422. (in Russian)

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

Ligun A.A. "Sharp inequalities for spline-functions and the best quadrature formulas for certain classes of functions", Mat. zametki, 1976; 19(6): pp. 913-926. (in Russian)

Ligun A.A. "On inequalities between norms of derivatives of periodic functions", Mat. zametki, 1983; 33(3): pp. 385-391. (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)

Kofanov V.A. "On sharp inequalities of Bernstein type for splines", Ukrainian Math. J., 2006; 58(10): pp. 1357-1367. (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)

Babenko V.F., Zontov V.A. "Inequalities of Bernstein type for splines defined on the real domain", Ukrainian Math. J., 2011; 63(5): pp. 603-611. (in Russian)

Babenko V.F., Spektor S.A. "Inequalities of Bernstein type for splines in $$$L_2(\mathbb{R})$$$ space", Dnipr. Univ. Math. Bull., 2008; 16(6/1): pp. 21-27. (in Russian)

Hermander L. Linear differential operators with partial derivatives, Mir, Moscow, 1965; 380 p. (in Russian)

Volevich L.R., Paneyakh B.P. "Certain spaces of generalized functions and inclusion theorems", Uspekhi mat. nauk, 1965; 20(1): pp. 3-74. (in Russian)

Mikhajlets V.A., Murach A.A. Hermander spaces, interpolation and elliptic problems, Kyiv, 2010; 372 p. (in Russian)

Strelkov N.A. "Projectively-net widths and lattice packings", Mat. sb., 1991; 182(10): pp. 1513-1533. (in Russian)

Strelkov N.A. "Universally optimal wavelets", Mat. sb., 1997; 188(1): pp. 147-160. (in Russian)

Chui K. Introduction to wavelets, Moscow, 2008. (in Russian)


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ISSN (Online): 2518-7996
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