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International Journal of Analysis
Volume 2015, Article ID 478345, 4 pages
http://dx.doi.org/10.1155/2015/478345
Research Article

Error Estimation of Functions by Fourier-Laguerre Polynomials Using Matrix-Euler Operators

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India

Received 6 July 2015; Revised 18 August 2015; Accepted 23 August 2015

Academic Editor: Dong Ye

Copyright © 2015 M. L. Mittal and Mradul Veer Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Various investigators have studied the degree of approximation of a function using different summability (Cesáro means of order : , Euler , and Nörlund ) means of its Fourier-Laguerre series at the point after replacing the continuity condition in Szegö theorem by much lighter conditions. The product summability methods are more powerful than the individual summability methods and thus give an approximation for wider class of functions than the individual methods. This has motivated us to investigate the error estimation of a function by -transform of its Fourier-Laguerre series at frontier point , where is a general lower triangular regular matrix. A particular case, when is a Cesáro matrix of order 1, that is, , has also been discussed as a corollary of main result.