A note on the absoute indexed norlund summability

Abstract

In the present article, we have established a result on indexed Norlund summability factors by generalizing a theorem of Mishra and Sivastava [5] on Cesaro summabilty factors.

A Note on Generalized Indexed Norlund Summability Factor of an Infinite Series

“…If (Y n ) is a positive non-decreasing sequence and there be sequences {β n } and {µ n } such that the conditions 2.1 to 2.5 along with the conditions 4.1 and 4.2 are satisfied then the series ∞ n=1 a n µ n is summable |N, q n , α n ; δ| k , k ≥ 1, δ ≥ 0, under the conditions 3.1 to 3.4.Thus, our result generalizes the result of Mishra and Srivastava [13] and Padhy et. al [14].…”

“…Very recently, Padhy et al[14] have proved a theorem on |N, q n | k -summability by extending theorem 2.4, in the following form: Theorem 2.5. Let for a positive non-decreasing sequence (Y n ),there be sequences {β n } and {µ n } satisfying the conditions 2.1 to 2.5 and {q n } be a sequence with {q n } ∈ R + such that…”