Sharp inequalities connected with estimates for approximations of periodic functions by means of moduli of continuity of their derivatives of odd order with different steps

被引：0

作者：

Vinogradov O.L.

Zhuk V.V.

机构：

来源：

Journal of Mathematical Sciences | 2000年 / 101卷 / 2期

关键词：

Periodic Function; Trigonometric Polynomial; Extremal Function; Bernoulli Polynomial; Require Assertion;

D O I：

10.1007/BF02672177

中图分类号：

学科分类号：

摘要：

Some inequalities similar to the Jackson theorem and the Landau-Hadamard-Kolmogorov theorem for the best approximations and moduli of continuity of the derivatives of odd order with different steps are established. The inequalities are sharp if the norm is uniform. Bibliography: 4 titles. © 2000 Kluwer Academic/Plenum Publishers.

引用

页码：2914 / 2929

页数：15

共 10 条

[1] Sharp inequalities for moduli of continuity of different orders and best approximations of periodic functions by trigonometric polynomials and splines
Vinogradov, OL
Zhuk, VV
[J]. DOKLADY MATHEMATICS, 2003, 67 (02) : 242 - 245
[2] SOME SHARP INEQUALITIES BETWEEN BEST APPROXIMATIONS OF PERIODIC FUNCTIONS AND MODULI OF CONTINUITY OF HIGHEST ORDERS
ZHUK, VV
[J]. VESTNIK LENINGRADSKOGO UNIVERSITETA SERIYA MATEMATIKA MEKHANIKA ASTRONOMIYA, 1978, (04): : 35 - 42
[3] Sharp Estimates for Deviations of Linear Approximation Methods for Periodic Functions by Linear Combinations of Moduli of Continuity of Different Order
O. L. Vinogradov
V. V. Zhuk
[J]. Journal of Mathematical Sciences, 2003, 114 (5) : 1628 - 1656
[4] Sharp estimates for the norms of differences in terms of the norms of the derivatives and the best majorants of moduli of continuity of periodic functions
Vinogradov O.L.
Zhuk V.V.
[J]. Journal of Mathematical Sciences, 2002, 112 (1) : 3967 - 3991
[5] On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives
Babushkin M.V.
Vinogradov O.L.
[J]. Journal of Mathematical Sciences, 2022, 261 (3) : 353 - 365
[6] Sharp estimates for the deviation of the mean value of a periodic function in terms of moduli of continuity of higher order
Vinogradov O.L.
Zhuk V.V.
[J]. Journal of Mathematical Sciences, 2001, 106 (3) : 2901 - 2918
[7] Sharp Estimates for the Best Approximations of Smooth Functions in C2π in Terms of Linear Combinations of the Modules of Continuity of Their Derivatives
Yu. P. Babich
T. F. Mikhaylova
[J]. Ukrainian Mathematical Journal, 2022, 74 : 651 - 655
[8] SHARP ESTIMATES FOR THE BEST APPROXIMATIONS OF SMOOTH FUNCTIONS IN C2π IN TERMS OF LINEAR COMBINATIONS OF THE MODULES OF CONTINUITY OF THEIR DERIVATIVES
Babich, Yu P.
Mikhaylova, T. F.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2022, 74 (04) : 651 - 655
[9] On the equivalence of some relations in different metrics between norms, best approximations, and moduli of smoothness of periodic functions and their derivatives
Il'yasov, Niyazi Aladdin
[J]. TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2018, 24 (04): : 176 - 188
[10] Order equalities in the spaces Lp(T), 1 < p < ∞, for best approximations and moduli of smoothness of derivatives of periodic functions with monotone Fourier coefficients
Il'yasov, Niyazi Aladdin Ogly
[J]. TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2022, 28 (04): : 103 - 120

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