On moduli of smoothness and averaged differences of fractional order-Reference-Cited by-同舟云学术

On moduli of smoothness and averaged differences of fractional order

Published:2017-08-01 Issue:4 Volume:20 Page:988-1009
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Kolomoitsev Yurii¹

Affiliation:

1. Institut für Mathematik , Universität zu Lübeck Ratzeburger Allee 160 23562 , Lübeck , Germany

Abstract

Abstract We consider two types of fractional integral moduli of smoothness, which are widely used in the theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli of smoothness. It turns out that for the fractional integral moduli of smoothness some pathological effects arise.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0051/pdf

Reference30 articles.

1. R. Akgün, Realization and characterization of modulus of smoothness in weighted Lebesgue spaces. St. Petersburg Math. J. 26, No 5 (2015), 741–756.

2. P.L. Butzer, H. Dyckhoff, E. Görlich, R.L. Stens, Best trigonometric approximation, fractional order derivatives and Lipschitz classes. Can. J. Math. 29 (1977), 781–793.

3. R.A. DeVore, G.G. Lorentz, Constructive Approximation. Springer-Verlag, New York (1993).

4. Z. Ditzian, V. Hristov, K. Ivanov, Moduli of smoothness and K-functional in Lp, 0 < p < 1. Constr. Approx. 11 (1995), 67–83.

5. V.I. Ivanov, Direct and inverse theorems of approximation theory in the metrics Lp for 0 < p < 1. Math. Notes18, No 5 (1975), 972–982.

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