Using infinite matrices to approximate functions of class Lip(α, p) using trigonometric polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:326

Article

Mittal, M. L. ; Rhoades, B. E. ; Mishra, V. N. ; Singh, Uaday

关键词: class Lip(alpha, p);    trigonometric approximation;    Lp-norm;   

DOI  :  10.1016/j.jmaa.2006.03.053

来源: Elsevier

【 摘 要 】

Given a function f in the class Lip(a, p) (0 < a < 1, p >= 1), Chandra [P. Chandra, Trigonometric approximation of functions in L-p-norm, J. Math. Anal. Appl. 275 (2002) 13-26] approximated such an f by using trigonometric polynomials, which are the nth terms of either certain weighted mean or Norlund mean transforms of the Fourier series representation for f. He showed that the degree of its approximation is O(n(-alpha)). In this paper we obtain the same degree of approximation for a more general class of lower triangular matrices, and deduce some of the results of [P. Chandra, Trigonometric approximation of functions in Lp-norm, J. Math. Anal. Appl. 275 (2002) 13-26] as corollaries. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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