Weighted gamma-K-functional and gamma-Modulus of Smoothness on the Semiaxis

zbMATH Open1379.41008arXiv1305.5490MaRDI QIDQ4597101

Zoltán Markó

Publication date: 11 December 2017

Abstract: In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of generalized Sobolev spaces, K-functionals and moduli of smoothness. We prove theorems for estimating these things with each other, in the case of first order we prove equivalence. We remark some possible applications and other generalizations too.

Full work available at URL: https://arxiv.org/abs/1305.5490

zbMATH Keywords

weighted modulus of smoothnessweighted \(K\)-functional\(\gamma\)-relative differentiationLaguerre-weight

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10)

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