We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in -norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in -norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.
In the present paper we consider a new class of sequences called GM(β,r), which is the generalization of a class defined by Tikhonov in [15]. We obtain sufficient and necessary conditions for uniform convergence of weighted trigonometric series with (β,r)-general monotone coefficients.
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].
We generalize and improve in some cases the results of Mahapatra and Chandra [7]. As a measure of Hölder norm approximation, generalized modulus-type functions are used.
In this paper we essentially extend the Leindler’s results concerning the uniform convergence and boundedness of a certain class of sine series.
A new class of rest bounded second variation sequences is defined. Some relationships between classes of considered sequences are proved. The results of Leindler [3] and author [8] are extended to our new class.
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.
We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.
We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of S. Lal [Appl....
We show the results corresponding to theorems of S. Lal [Appl. Math. Comput., 209 (2009) 346-350] on the rate of approximation of functions from the generalized integral Lipschitz classes by matrix summability means of their Fourier series as well as to the authors theorems [Acta Comment. Univ. Tartu. Math., 13 (2009), 11-24] also on such approximations.
We generalize and extend the some results of the paper [6]. Considering a wider class of function and more general means we obtain the results of the V. Totik type [8, 9].
We consider the class GM(₂β) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
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