Absolute summability factor \varphi-|C,1;\delta|_k of infinite series

2016 ◽  
Vol 10 ◽  
pp. 1129-1136 ◽  
Author(s):  
Smita Sonker ◽  
Alka Munjal
Keyword(s):  
Infinite Series ◽  
Absolute Summability ◽  
Summability Factor

scholarly journals Characterization on some absolute summability factors of infinite series

1999 ◽  
Vol 22 (4) ◽  
pp. 817-822
Author(s):  
W. T. Sulaiman
Keyword(s):  
Infinite Series ◽  
General Theorem ◽  
Absolute Summability ◽  
Summability Factors ◽  
Absolute Summability Factors

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.

scholarly journals Index Summability of an Infinite Series Using δ-Quasi Monotone Sequence

2015 ◽  
Vol 11 ◽  
pp. 21-29
Author(s):  
Mahendra Misra ◽  
B.P. Padhy ◽  
Santosh Kumar Nayak ◽  
U.K. Misra
Keyword(s):  
Infinite Series ◽  
Monotone Sequence ◽  
Summability Factor

A result concerning absolute indexed Summability factor of an infinite series using δ-Quasi monotone sequence has been established.

scholarly journals A summability factor theorem for absolute summability involving almost increasing sequences

2004 ◽  
Vol 2004 (69) ◽  
pp. 3793-3797 ◽  
Author(s):  
B. E. Rhoades ◽  
Ekrem Savaş
Keyword(s):  
Sufficient Conditions ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Summability Factor ◽  
Factor Theorem ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

We obtain sufficient conditions for the series∑anλnto be absolutely summable of orderkby a triangular matrix.

Absolute summability of infinite series on a scale of Abel type summability methods

1968 ◽  
Vol 64 (2) ◽  
pp. 377-387 ◽  
Author(s):  
Babban Prasad Mishra
Keyword(s):  
Infinite Series ◽  
Open Interval ◽  
Absolute Summability ◽  
Finite Limit ◽  
Summability Methods ◽  
Image Position

Suppose that λ > − 1 and thatIt is easy to show thatWith Borwein(1), we say that the sequence {sn} is summable Aλ to s, and write sn → s(Aλ), if the seriesis convergent for all x in the open interval (0, 1)and tends to a finite limit s as x → 1 in (0, 1). The A0 method is the ordinary Abel method.

On Absolute Summability by Riesz and Generalized Cesàro Means. I

1970 ◽  
Vol 22 (2) ◽  
pp. 202-208 ◽  
Author(s):  
H.-H. Körle
Keyword(s):  
Infinite Series ◽  
Absolute Summability ◽  
Partial Sums ◽  
Cesàro Means ◽  
Riesz Means ◽  
Cesaro Means ◽  
Cesáro Means ◽  
Image Position ◽  
Generalized Cesàro Means

1. The Cesàro methods for ordinary [9, p. 17; 6, p. 96] and for absolute [9, p. 25] summation of infinite series can be generalized by the Riesz methods [7, p. 21; 12; 9, p. 52; 6, p. 86; 5, p. 2] and by “the generalized Cesàro methods“ introduced by Burkill [4] and Borwein and Russell [3]. (Also cf. [2]; for another generalization, see [8].) These generalizations raise the question as to their equivalence.We shall consider series(1)with complex terms an. Throughout, we will assume that(2)and we call (1) Riesz summable to a sum s relative to the type λ = (λn) and to the order κ, or summable (R, λ, κ) to s briefly, if the Riesz means(of the partial sums of (1)) tend to s as x → ∞.

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