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On the Uniform Approximation of Analytic Functions By Fejer Type Sums of Faber Series

T. TUNC*, M. KUCUKASLAN**

*-** Mersin University Faculty of Science and Literature, Department of Mathematics, Mersin, TURKEY.

Periodicity:January - March'2012
DOI : https://doi.org/10.26634/jmat.1.1.1663

Abstract

In this paper, a submethod of De la Vallee-Poussin method is defined. The deviation of any function analytic in a region with bounded variation boundary from the polynomials obtained by applying the submethod to the Faber series of the function is estimated.

Keywords

De la Vallee-Poussin sums, Faber series, Radon curves, 2000.

How to Cite this Article?

Tunc, T., and Kucukaslan, M. (2012). On The Uniform Approximation of Analytic Functions by Fejer Type Sums of Faber Series. i-manager’s Journal on Mathematics, 1(1), 8-11. https://doi.org/10.26634/jmat.1.1.1663

References

[1]. Abdullayev, F.G., Zaderey, N., & Zaderey, P. (2010). On the Approximation of Analytic Functions by Fejer Sums of Faber Series. Math. Analysis Differential Equations and Application, (pp. 13-18). Sunny Beach, Bulgaria.

[2]. Armitage, H.D., & Maddox, I.J. (1989). A new type of Cesaro Mean. Analysis 9, 195-204.

[3]. Faber, G. (1903). Über Polynomische Entwickelungen. Math. Ann., 57, 389-408.

[4]. Maddox, I.J. (1970). Elements of Functional Analysis. Cambridge at the University Press.

[5]. Sidon, S. (1939). Hinreichende Bedingungen fur den Fourier-carakter einer trigonometrisehen Reine H.J. London Math. Soc., 14(2), 158-160.

[6]. Stechkin, S.B. (1961). The Approximation of Priodic Functions by Fejer Sums. Collection of Articles on Linear Methods of Summation of Fourier Series, Trudy Math. Inst. Steklov., Acad.Sci. USSR, Moscow. 62, 48-60.

[7]. Suetin, P.K. (1998). Series of Faber Polynomials. Gordon and Breach Science Publishers.

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