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Analysis

International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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2196-6753
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Volume 34, Issue 3

An analogue of Leindler's theorem for hexagonal Fourier series

Ali Guven
Published Online: 2014-08-01 | DOI: https://doi.org/10.1515/anly-2012-1241

Abstract.

Let ${ℳ}_{\alpha }$ be the class of moduli of continuity defined by Leindler in [Studia Sci. Math. Hungar. 14 (1979), 431–439], and ${H}^{{\omega }_{\alpha }}\left(\overline{\Omega }\right)$ be the generalized Hölder class of functions on the closure of the regular hexagon Ω, where $0<\alpha \le 1$ and ${\omega }_{\alpha }\in {ℳ}_{\alpha }$. The difference $f-{𝒱}_{n}^{\lambda }\left(f\right)$ is estimated in the uniform norm ${\parallel ·\parallel }_{C\left(\overline{\Omega }\right)}$ and in the generalized Hölder norm ${\parallel ·\parallel }_{{\omega }_{\beta }}$, where ${𝒱}_{n}^{\lambda }\left(f\right)$ is the nth generalized de la Vallée-Poussin mean of hexagonal Fourier series of $f\in {H}^{{\omega }_{\alpha }}\left(\overline{\Omega }\right)$ and $0\le \beta <\alpha \le 1$.

MSC: 41A25; 42A10; 42B08

Revised: 2014-04-18

Accepted: 2014-05-21

Published Online: 2014-08-01

Published in Print: 2014-08-01

Citation Information: Analysis, Volume 34, Issue 3, Pages 283–297, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747,

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