International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 1-8
Approximation by weighted means of Walsh-Fourier series
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 and, in particular, in by weighted means of their Walsh-Fourier series, where and . For the case , is interpreted to be , the collection of uniformly continuous functions over the unit interval . We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.