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Acta Mathematica Hungarica
Volume/Issue:
Volume 133: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-0063-1
Author:
Péter Kórus

. 128 369 – 380 10.1007/s10474-010-9217-4 . [2] Móricz , F. 2009 On the uniform convergence of sine integrals J. Math. Anal

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Acta Mathematica Hungarica
Volume/Issue:
Volume 93: Issue 1-2
DOI:
https://doi.org/10.1023/a:1013865315680
Author:
U. Goginava

Abstract  

We study the uniform convergence of Walsh-Fourier series of functions on the generalized Wiener class BV (p(n)↑∞)

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 26: Issue 1
DOI:
https://doi.org/10.1007/bf01875883
Author:
J. Ewert

The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 63: Issue 2
DOI:
https://doi.org/10.1007/s10998-011-8205-y
Author:
Péter Kórus

Abstract  

Chaundy and Jolliffe proved their classical theorem on the uniform convergence of sine series with monotone coefficients in 1916. Lately, it has been generalized using classes MVBVS and SBVS2 instead of monotone sequences. In two variables, the class MVBVDS was studied under the uniform regular convergence of double sine series. We shall generalize those results defining a new class of double sequences for the coefficients.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 108: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-005-0217-8
Authors:
R. J. Le
and
S. P. Zhou
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Acta Mathematica Hungarica
Volume/Issue:
Volume 88: Issue 1-2
DOI:
https://doi.org/10.1023/a:1006796325956
Author:
S. Naimpally
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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 56: Issue 1
DOI:
https://doi.org/10.1556/012.2019.56.1.1422
Author:
Gvantsa Shavardenidze

Abstract

In 1971 Onnewer and Waterman establish a sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In this paper we consider different classes of functions of generalized bounded oscillation and in the terms of these classes there are established sufficient conditions for uniform convergence of Cesàro means of negative order.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 75: Issue 4
DOI:
https://doi.org/10.1023/a:1006593505036
Authors:
H.-P. Künzi
and
S. Romaguera
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Acta Mathematica Hungarica
Volume/Issue:
Volume 91: Issue 1-2
DOI:
https://doi.org/10.1023/a:1010643229421
Authors:
L. Szili
and
P. Vértesi
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Analysis Mathematica
Volume/Issue:
Volume 1: Issue 4
DOI:
https://doi.org/10.1007/bf02333178
Author:
Е. Севастьянов

Abstract  

Let

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R_n [f] = \inf \left\{ {\mathop {\max }\limits_{ - \pi \leqq x \leqq \pi } \left| {f(x) - \frac{{P(x)}}{{Q(x)}}} \right|} \right\}$$ \end{document}
, whereP andQ denote polynomials (algebraic or trigonometric) of degree ≦n. Theorem 2a. If for a continuous 2π-periodic function f the condition
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{n = 1}^\infty {\frac{1}{n}R_n [f]< \infty }$$ \end{document}
 holds, then the Fourier series of f converges to f(x) uniformly. Theorem 2b. Let {β n } be a non-increasing sequence of positive numbers such that
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{n = 1}^\infty {\frac{1}{n}\beta _n = \infty }$$ \end{document}
 Then there exists a continuous 2π-periodic function f0 for which Rn[f0]≦βn for all n=1 and yet the Fourier series of f0 diverges at x=0.R n [f]may be replaced in these theorems byM n [f], whereM n [f] is the minimal uniform deviation off(x) from piecewise monotonie functionsМ n (х) of order ≦n.

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