A Summability Factor Theorem for Quasi-Power-Increasing Sequences

A Summability Factor Theorem for Quasi-Power-Increasing Sequences

Correspondence should be addressed to E. Savaş, [email protected] Received 23 June 2010; Revised 3 September 2010; Accepted 15 September 2010 Academic Editor: J. Szabados Copyright q 2010 E. Savaş. 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 ...

a generalized summability factor theorem for absolute summability and quasi   power increasing sequences

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.

a summability factor theorem for absolute summability involving quasi power increasing sequences

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

A summability factor theorem for absolute summability involving almost increasing sequences

A triangle is a lower triangular matrix with all principal diagonal entriesbeing nonzero. Given an almost increasing sequence {Xn} and a sequence {λn} satisfying certain conditions, we obtain sufficient conditions for the series ∑ anλn to be absolutely summable of order k ≥ 1 by a triangle T . As a corollary we obtain the corresponding result when T is a weighted mean matrix. Theorem 1 of this ...

Quasi β-power increasing sequences