APPROXIMATION OF |sin x| BY RATIONAL OPERATORS OF FEJÉR TYPE
Abstract
Rational Fourier series were constructed by M. M. Dzhrbashian in 1956. A compact representation of their Dirichlet kernel was also found. Later V. N. Rusak introduced rational operators of Fejér, de la Vallée Poussin and Jackson type. Partial sums of rational Fourier series, operators of de la Vallée Poussin and Jackson type are widely used for finding classes of functions, for which rational approximation is better than polynomial approximation. But in our opinion, rational operators of Fejér type are still unexpolred, so it’s interesting to investigate their approximation characteristics for elementary functions. The periodic function | sin | x plays almost the same role in approximation theory as the function |x |. In this article, we have obtained some exact and asymptotic ratios for approximation of | sin x | by Fejér-type rational operators.
About the Authors
E. A. Rovba
Yanka Kupala State University of Grodno
Belarus
Belarus
D. Sc. (Physics and Mathematics), Professor of the Department of Fundamental and Applied Mathematics, Faculty of Mathematics and Informatics
N. Yu. Kozlovskaya
Yanka Kupala State University of Grodno
Belarus
Belarus
5th year student
References
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