Inclusion of absolute summability domains of matrices Factorable matrices Summability method of Cesàro a b s t r a c t In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely conve...

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 we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.

the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.

In the year 1921, Nevanlinna [7] suggested and discussed an interesting method of summation called Nq-method. Moursund [5] applied this method for summation of Fourier series and its conjugate series. Later, Moursund [6] developed Nqp-method (where p is a positive integer) and applied it to pth derived Fourier series. Samal [9] discussed Nqαmethod (0 ≤ α < 1) and studied absolute Nqα-summabilit...