Various investigators such as Khan 1974 , Chandra 2002 , and Liendler 2005 have determined the degree of approximation of 2π-periodic signals functions belonging to Lip α, r class of functions through trigonometric Fourier approximation using different summability matrices with monotone rows. Recently, Mittal et al. 2007 and 2011 have obtained the degree of approximation of signals belonging to...

In this paper, an application to the approximation by wavelets has been obtained by using matrix-Cesàro (Λ · C1) method of Jacobi polynomials. The rapid rate of convergence of matrix-Cesàro method of Jacobi polynomials are estimated. The result of Theorem (6.1) of this research paper is applicable for avoiding the Gibbs phenomenon in intermediate levels of wavelet approximations. There are majo...

In this paper, a general theorem concerning absolute matrix summability is established by applying the concepts of almost increasing and δ-quasi-monotone sequences.

Mittal and Rhoades (1999–2001) andMittal et al. (2006) have initiated the studies of error estimates En( f ) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of a function ̃ f , conjugate to a periodic function f belonging to the weighted W(Lp,ξ(t))-class (p...

The present paper is concerned with the concept of the dual matrix sequences of the new sort which is introduced by Altay and Başar [2], for the ordinary summability methods. Thus, some classes of matrix sequences have been characterized as an application of the dual matrix sequences of the new sort. The last section of the paper is devoted to the inclusion theorems related to the original and ...

Correspondence should be addressed to E. Savaş, [email protected] Received 23 June 2010; Revised 3 September 2010; Accepted 15 September 2010 Academic Editor: J. Szabados Copyright q 2010 E. Savaş. 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 ...