In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.

1 The first four notes of this series appeared in these PROCEEDINGS, 14, 915-918 (1928); 15, 41-42 (1929); 16, 594-598 (1930); 17, 376-380 (1931). In these notes we were concerned exclusively with the methods of Hausdorff and Woronoi-Norlund. The results of the present note were communicated to the American Mathematical Society on April 14, 1933. Cf. also E. Hille, "Summation of Fourier Series,...