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International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 641-651

Some absolutely effective product methods

1Dept. of Math & Computer Science, Rani Durgavati University, Jabalpur 482001, India
2Dept. of Math & Computer Science, Kent State University, Kent 44242, Ohio, USA

Received 20 June 1991; Revised 24 March 1992

Copyright © 1992 Hindawi Publishing Corporation. 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.


It is proved that the product method A(C,1), where (C,1) is the Cesàro arithmetic mean matrix, is totally effective under certain conditions concerning the matrix A. This general result is applied to study absolute Nörlund summability of Fourier series and other related series.