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  • Author or Editor: László Leindler x
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Summary We establish an improvement of a recent theorem of S. M. Mazhar which is a generalization of our result and studies the embedding relation between the class W r H S ω, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions (see the precise definitions below).

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Abstract  

Our aim is to find the source why the logarithm sequences play the crucial role in the L 1-convergence of sine series. We define three new classes of sequences; one of them has the character of the logarithm sequences, the other two are the extensions of the class defined by Zhou and named Logarithm Rest Bounded Variation Sequences. In terms of these classes, extended analogues of Zhou’s theorems are proved.

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We show that the classical monotonicity conditions can be moderated in four theorems of P. Chandra.

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Abstract  

We verify a newer version of a certain embedding theorem pertaining to the relation being between strong approximation and a certain wide class of continuous functions. We also show that a new class of numerical sequences defined in this paper is not comparable to the class defined by Lee and Zhou, which is one of the largest among the classes being extensions of the class of monotone sequences.

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Our aim is to extend the validity domains of two important Bary- Stečkin lemmas from positive integers to certain real numbers.

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The aim of the paper is to analyze the relationship of some newly defined classes of numerical sequences to the important Sidon-Telyakovskiĭ class.

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Summary  

Recently we extended some interesting theorems of Konyushkov giving estimations for the best approximation by the coefficients of the Fourier series of the function in question. We replaced the monotone or quasi-monotone coefficient sequences by coefficient sequences of rest bounded variation. In this note both notions are generalized for such coefficient sequences where certain restriction is given only in terms of the "rest variation" of the sequence.

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