Approximation of functions by (C,2)(E,1) product summability method of Fourier series

Jitendra Kumar Kushwaha

Abstract


Various investigators such as Leindler [10], Chandra [1], Mishra et al. [7], Khan [11], Kushwaha [6] have determined the degree of approximation of  2 pai-periodic functions belonging to generalized Lipschitz class of functions through trigonometric Fourier approximation using different summability means.  Recently H.K. Nigam [12] has determined that the Fourier series is summable under the summability means (C,2)(E,1) but he did not find the degree of approximation of function belonging to various classes.  In  this paper a theorem concerning the degree of approximation of function  belonging to  class by (C,2)(E,1) product summability method of Fourier series  has been established which  in turn generalizes the result of  H.  K. Nigam [12].


Keywords


Degree of approximation; Fourier series; Pruduct summability methods.

Full Text:

PDF

References


P. Chandra , Approximation by Nörlund operators, Mat. Vestnik, Vol. 8, 263-269, 1986.

P. Chandra, functions of classes and and their Riesz means, Riv. Mat. Univ. Parm, Vol. 4, No. 12, 275-282, 1986.

] P. Chandra , On the degree of approximation of a class of function by means of Fourier series , Acta Mathematica Hungarica, Vol. 52 , No. 3-4, 199-205, 1988.

A.B.S. Hollend, R.N. Mohapatra and B.N. Sahney , approximation of function by Euler means, Rendiconti di Mathematica (Rome)(2), Vol. 3, 341-355, 1983.

S. Lal and P.N. Singh, Degree o approximation of conjugate of function by (C,1)(E,1) means of conjugate series of Fourier series, Tamkang Journal of Mathematics, Vol. 33, No. 3, 269-274, 2002.

Lal and Kushwaha, Degree of approximation of Lipschitz Function by (C,1)(E,q) product Summability Method, Int. Math. Forum Vol.4 (no. 41-44), 2009, pp. 2101-2107.

V.N. Mishra and L. N. Mishra, Trigonometric Approximation by signals(Functions) in -norm, International Journal of Contemporary Mathematical Sciences , Vol. 7, No. 19, 2012, pp. 909-918.

R.N. Mohapatra and B.N. Sahney, Approximation of continuous function by their Fourier series, Mathemtica: Journal L’ Anlyse Numerique la Theorie de l’approxiamtion, Vol.10, 81-87, 1981.

R. N. Mohapatra and P. Chandra, Holder continuous function and their Euler, Borel and Taylor meas, Math. Cronicle (New Zealand), Vol. 11 81-96, 1988.

L. Leindler, Trigonometric Approximation in norm, Journal of Mathematical Analysis and Applicaiton, Vol. 302, No. 1, 2005, pp. 129-136.

H.H. Khan, On Degree of Approximation of a functions Belonging to class , Indian Journal of Pure and Applied Mathematics, Vol. 5, No. 2, 1974,pp. 132-136.

H.K. Nigam, On (C,2)(E,1) Product means of Fourier series, Electronic Journal of Mathematical Analysis an Application, Vol.1(2) July 2013, pp. 334-344.

E.C. Titchmarsh, The Theory of functions, Oxford University Press, 402-403, 1939.

G.H. Hardy, Divergent Series, Oxford University Press, Oxford, 1949.




DOI: http://dx.doi.org/10.23755/rm.v38i0.504

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Jitendra Kumar Kushwaha

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.