International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 1-8

Approximation by weighted means of Walsh-Fourier series

F. Móricz1 and B. E. Rhoades2

1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, Hungary
2Department of Mathematics, Indiana University, Bloomington 47405, Indiana, USA

Received 26 April 1993; Revised 20 February 1995

Copyright © 1996 F. Móricz and B. E. Rhoades. 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.


We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1p. For the case p=, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.