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In this paper, we introduce some new classes of functions and investigate the embedding relations among these classes. Our results generalize the related results of Leindler [3] and Yu-Zhou [9].
Abstract
We present necessary and sufficient conditions for double sine, sinecosine, cosine-sine and double cosine series in terms of coefficients that their sums belong to double Lipschitz classes. Some classical results on single trigonometric series and some new results of Fülöp [2] on double trigonometric series are extended.
Abstract
We construct a new kind of rational operator which can be used to approximate functions with endpoints singularities by algebric weights in [−1,1], and establish new direct and converse results involving higher modulus of smoothness and a very general class of step functions, which cannot be obtained by weighted polynomial approximation. Our results also improve related results of Della Vecchia [5].
We generalize five theorems of Leindler on the relations among Fourier coefficients and sum-functions under the more general N BV condition
Abstract
In this paper, we generalize two important results of Bagota and Móricz [1], and generalize our earlier results in [6] from one-variable to two-variable case. As special applications, we prove that the generalized jump of f(x, y) at some point (x 0, y 0) can be determined by the higher order mixed partial derivatives of the Abel-Poisson mean of double Fourier series and the higher order mixed partial derivatives of the Abel-Poisson means of the three conjugate double Fourier series.
Abstract
We introduce a new kind of double sequences named MVBVDS and some new classes of weight functions to study the weighted integrability of the double trigonometric series. Several results of Chen, Marzuq, Móricz, Ram and Singh Bhatia (see [2]–[10]) are generalized and some new results are established.
