Abstract
In the present article, we have established a result on generalized indexed absolute Norlund summability factor by generalizing results of Mishra and Srivastava on indexed absolute Cesaro summabilty factors and Padhy et.al. on the absolute indexed Norlund summability.
Highlights
IntroductionIn 1930, J.M.Whittaker [18] was the 1st to establish a result on the absolute summability of Fourier series and in 1932, M
We have established a result on generalized indexed absolute Norlund summability factor by generalizing results of Mishra and Srivastava on indexed absolute Cesaro summabilty factors and Padhy et al on the absolute indexed Norlund summability
In 1930, J.M.Whittaker [18] was the 1st to establish a result on the absolute summability of Fourier series and in 1932, M
Summary
In 1930, J.M.Whittaker [18] was the 1st to establish a result on the absolute summability of Fourier series and in 1932, M. Have established results on indexed summability factors of an infinite series. Let an be a given infinite series with sequence of partial sums {sn}. Let tnα be the nth (C, α) mean (with order α > −1) of the sequence {sn} and is given by tαn =. Let tn be the nth (C, 1)- mean of the sequence {sn} and is given by 1n tn = n + 1 sk, k=0 the series anis said to be summable |C, 1|k, k ≥ 1, [3] if (n)k−1|tn − tn−1|k < ∞. The series an is said to be summable |N, qn| if the sequence {Tn} is of bonded variation i.e; |Tn − Tn−1| is convergent. Further any sequence {αn} of positive numbers the series an is said to be summable |N, qn, αn|k, k ≥ 1 if (αn)k−1|Tn − Tn−1|k < ∞.
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