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- Zeev Ditzian, S. Tikhonov
- Journal of Approximation Theory
- 2005

- Zeev Ditzian
- Journal of Approximation Theory
- 2006

- Zeev Ditzian, A. V. Prymak
- Journal of Approximation Theory
- 2008

- Feng Dai, Zeev Ditzian, S. Tikhonov
- Journal of Approximation Theory
- 2008

For trigonometric polynomials on [− , ] ≡ T , the classical Jackson inequalityEn(f )p C r (f, 1/n)p was sharpened by M. Timan for 1<p<∞ to yield n−r { n ∑ k=1 ksr−1Ek(f )p }1/s C r (f, n−1)p where s =max(p, 2). In this paper a general result on the relations between systems or sequences of best approximation and appropriate measures of smoothness is given.… (More)

- Z. Ditzian
- 2007

About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of… (More)

- Eduard Belinsky, Feng Dai, Zeev Ditzian
- Journal of Approximation Theory
- 2003

- Z. Ditzian
- 2007

About twenty years ago the measure of smoothness ω φ (f, t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. MSC: 41A10, 41A17, 41A25, 41A27, 41A30, 41A36, 41A40, 41A50, 41A63, 26A15, 26B35, 26B05, 42C05, 26A51, 26A33, 46E35 keywords: Moduli of… (More)

- Feng Dai, Zeev Ditzian
- Journal of Approximation Theory
- 2004

Rate of approximation of combinations of averages on the spheres is shown to be equivalent to K-functionals yielding higher degree of smoothness. Results relating combinations of averages on rims of caps of spheres are also achieved. © 2004 Elsevier Inc. All rights reserved. MSC: 41A17; 41A63; 26B33; 46E35

- Z. DITZIAN, A. V. PRYMAK
- 2005

For Lp spaces on Td, Rd and Sd−1 sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on Td, Rd and Sd−1) for which M(u1/q) is convex for some q, 1 < q ≤ 2, where M(u) is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

- Zeev Ditzian
- Journal of Approximation Theory
- 2010