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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 267383, 6 pages
http://dx.doi.org/10.1155/2014/267383
Research Article

Approximation of Signals (Functions) by Trigonometric Polynomials in -Norm

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

Received 13 January 2014; Revised 13 March 2014; Accepted 13 March 2014; Published 9 April 2014

Academic Editor: A. Zayed

Copyright © 2014 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

Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix does not have monotone rows. In this paper, the first author continues the work in the direction for to be a -matrix. We extend two theorems on summability matrix of Deger et al. (2012) where they have extended two theorems of Chandra (2002) using -method obtained by deleting a set of rows from Cesàro matrix . Our theorems also generalize two theorems of Leindler (2005) to -matrix which in turn generalize the result of Chandra (2002) and Quade (1937).