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http://dx.doi.org/10.7858/eamj.2021.019

DEGREE OF APPROXIMATION OF FUNCTIONS OF CLASS Zygω(α, γ) BY CESARO MEANS OF FOURIER SERIES  

Kim, Jaeman (Department of Mathematics Education, Kangwon National University)
Publication Information
East Asian mathematical journal / v.37, no.3, 2021 , pp. 289-293 More about this Journal
Abstract
In this paper, we investigate the degree of approximation of a function f belonging to the generalized Zygmund class Zygω(α, γ) by Cesaro means of its Fourier series.
Keywords
Degree of approximation; generalized Zygmund class $Zyg^{\omega}({\alpha},{\gamma})$; Cesaro means; Fourier series;
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1 Titchmarsh, E.C.: Theory of Functions, Oxford Univ. Press, Oxford, 1939.
2 Moricz, F.: Enlarged Lipschitz and Zygmund classes of functions and Fourier transformations, East J. Approx. 16 (2010), no. 3, 259-271.
3 Moricz, F. and Nemeth, J.: Generalized Zygmund classes of functions and strong approximation by Fourier series, Acta Sci. Math. 73 (2007), no. 3-4, 637-647.
4 Zygmund, A.: Trigonometric Series, Vol. 1, Cambridge Univ. Press, Cambridge, 1959.
5 Mittal, M.L., Rhoades, B.E., Mishra, V.N. and Singh, U.: Using infinite matrices to approximate functions of class Lip(α, p) using trigonometric polynomials, J. Math. Anal. Appl. 326 (2007), 667-676.   DOI
6 Chandra, P.: Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002), 13-26.   DOI
7 Leindler, L.: Strong approximation and generalized Zygmund class, Acta Sci. Math. 43 (1981), no. 3-4, 301-309.
8 Khan, H.H.: On degree of approximation of functions belonging to class Lip(α, p), Indian J. Pure Appl. Math. 5 (1974), 132-136.
9 Lal, S.: Approximation of functions belonging to the generalized Lipschitz class by C1Np summability method of Fourier series, Appl. Math. Comput. 209 (2009), 346-350.   DOI
10 Lal, S. and Mishra, A.: Approximation of functions of class Lip(α, r),(r ≥ 1), by (N, pn)(E, 1) summability means of Fourier series, Tamkang J. Math. 45 (2014), 243-250.   DOI