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The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fejér means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression. In one-dimensional cases, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of a complex plane. [ABSTRACT FROM AUTHOR]

We estimate the pointwise approximation of periodic func- tions belonging to Lp(ω)β-class, where ω is an integral modulus of conti- nuity type function associated with f, using product means of the Fourier series of f generated by the product of two general linear operators. We also discuss the case p = 1 separately. This case has not been mentioned in the earlier results given by various authors. The deviations obtained in our theorems are free from p and more sharper than the earlier results. [ABSTRACT FROM AUTHOR]

Abstract: Analysis of signals or time functions are of great importance, because it convey information or attributes of some phenomenon. In this paper, we consider the functions/signals defined in terms of their integral modulus of continuity and approximate them by matrix means of their trigonometric Fourier series. The error of approximation obtained in this paper depends on the integral modulus of continuity of the signal. We also discuss an example to show the application of the result in the situation when the Fourier series of the signal has Gibbs phenomenon. We also discuss some corollaries of our theorems. [Copyright &y& Elsevier]

We extend the results of Xh. Z. Krasniqi (Acta Comment. Univ. Tartu Math. 17:89-101, 2013) and the authors (Acta Comment. Univ. Tartu Math. 13:11-24, 2009; Proc. Est. Acad. Sci. 67:50-60, 2018) to the case when considered function is 2π/r-periodic and the measure of approximation depends on r-differences of the entries of the considered matrices. [ABSTRACT FROM AUTHOR]