# Search Results

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

## Abstract

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

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.

## 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 SBVS_{2} 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.

## 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.

## Abstract

Let

*P*and

*Q*denote polynomials (algebraic or trigonometric) of degree ≦

*n*. Theorem 2a. If for a continuous 2π-periodic function f the condition

*β*

_{ n }} be a non-increasing sequence of positive numbers such that

_{0}for which R

_{n}[f

_{0}]≦β

_{n}for all n=1 and yet the Fourier series of f

_{0}diverges at x=0.

*R*

_{ n }

*[f]*may be replaced in these theorems by

*M*

_{ n }

*[f]*, where

*M*

_{ n }

*[f]*is the minimal uniform deviation of

*f(x)*from piecewise monotonie functions

*М*

_{ n }

*(х)*of order ≦

*n*.