Abstract
A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.
Highlights
Let an be an infinite series with partial sum sn
Let σnδ and ηδn denote the nth Cesàro mean of order δ(δ > −1) of the sequences {sn} and {nan}, respectively
For pn = 1, N, pn k summability is equivalent to C, 1 k summability
Summary
Let an be an infinite series with partial sum sn. Let σnδ and ηδn denote the nth Cesàro mean of order δ(δ > −1) of the sequences {sn} and {nan}, respectively. The series an is said to be summable |C, δ|k, k ≥ 1, if. For pn = 1, N, pn k summability is equivalent to C, 1 k summability. The series an is said to be summable N, pn, φn k, k ≥ 1, if (Sulaiman [4]). Let {pn}, {qn}, and {φn} be sequences of real positive constants. Let tn denote the (N, pn)-mean of the series an. If. the series an n is summable N, qn, φn k, k ≥ 1, where ∆fn = fn −fn+1 for any sequence {fn} and n.
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