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Abstract  

A new class of rest bounded second variation sequences is introduced. Leindler’s result [7] for such wider class of sequences is proved.

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Abstract  

We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. M�ricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3].

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We generalize five theorems of Leindler on the relations among Fourier coefficients and sum-functions under the more general N BV condition

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Abstract  

The class of infinity mean of rest bounded variation sequences, briefly IMRBVS is introduced and it is shown that IMRBVS ≠
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bar \gamma _m$$ \end{document}
MRBVS and IMRBVS ≠ γm * MRBVS. Some of Leindler’s results from [10] are strengthened.
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Abstract  

We study when sums of trigonometric series belong to given function classes. For this purpose we describe the Nikol’skii class of functions and, in particular, the generalized Lipschitz class. Results for series with positive and general monotone coefficients are presented.

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Abstract

We prove that the conjugate convolution operators can be used to calculate jumps for functions. Our results generalize the theorems established by He and Shi. Furthermore, by using Lukács and Móricz's idea, we solve an open question posed by Shi and Hu.

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Abstract

In 1953 Nash [7] introduced the class of functions Φ. In this paper the behaviour of generalized Cesàro (C,α n)-means (α n∊(−1,0)) of trigonometric Fourier series of the classes H ω∩Φ in the space of continuous functions is studied. The sharpness of the results obtained is shown.

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Abstract  

We describe the functions from Nikol’skii class in terms of behavior of their Fourier coefficients. Results for series with general monotone coefficients are presented. The problem of strong approximation of Fourier series is also studied.

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Abstract  

We generalize some old and new results on the determination of jumps of a periodic, Lebesgue integrable function f at each point of discontinuity of first kind in terms of the partial sums of the conjugate series to the Fourier series of f in [1], and in terms of the Abel-Poisson means in [2], to some more general linear operators which satisfy some certain conditions. The linear operators in discussion include the Fejér means, de la Vallée-Poussin means, and Bernstein-Rogosinski sums.

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