Abstract
We establish a summability factor theorem for summability , where is lower triangular matrix with nonnegative entries satisfying certain conditions. This paper is an extension of the main result of the work by Rhoades and Savaş (2006) by using quasi -increasing sequences.
Highlights
Rhoades and Savas 1 obtained sufficient conditions for anλn to be summable |A, δ|k, k ≥ 1 by using almost increasing sequence
Let bv[0] bv ∩ c0, where c0 denotes the set of all null sequences
It should be noted that every almost increasing sequence is quasi β-power increasing sequence for any nonnegative β, but the converse need not be true as can be seen by taking an example, say γn n−β for β > 0 see, 4
Summary
We establish a summability factor theorem for summability |A, δ|k, where A is lower triangular matrix with nonnegative entries satisfying certain conditions. This paper is an extension of the main result of the work by Rhoades and Savas 2006 by using quasi f-increasing sequences
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