Abstract
In this note we introduce a new method of absolute summability. A general theorem is given. Several results are also deduced.
Highlights
L’et be an infinite series with partial sums s
In the special case in which pn A,I, r > 1, where A is the coefficient of z in the power series expansion of (1 z)-’-1 for Izl < 1, IN, p,.,ltc summability reduces to IC, r[k summability
In order that A (Ik;Ik), it is necessary that a,v 0(1) (.,{,)
Summary
L’et be an infinite series with partial sums s. DEFINITION 1 (Sulaiman [5]). In the special case in which pn A,-I, r > 1, where A is the coefficient of z in the power series expansion of (1 z)-’-1 for Izl < 1, IN, p,.,ltc summability reduces to IC, r[k summability. The series a is said to be summable IR, p.lk, IN, p.Ik, k > 1 fBor [2] & [1]), if. We assume {,}, {a,} and {/,} be sequences of positive real constants. Let {p,}, {q,} be sequences of positive real constants such that q E M We say that a, is summable IN,/, 1, k > 1, if DEFINITION 3 (Sulaiman [6]). The series a, is said to be summable IN, p,, On Ik, k k 1, if
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