On generalized absolute Cesàro summability factors
© Tuncer; licensee Springer 2012
Received: 23 December 2011
Accepted: 17 October 2012
Published: 30 October 2012
In this paper, a known theorem dealing with summability factors has been generalized for summability factors. Some results have also been obtained.
MSC:40D15, 40F05, 40G99.
If we take , then summability reduces to summability (see ).
2 Known result
In , we have proved the following theorem dealing with summability factors of infinite series.
then the series is summable .
3 The main result
The aim of this paper is to generalize Theorem A for summability. We shall prove the following theorem.
then the series is summable . It should be noted that if we take , then we get Theorem A.
We need the following lemmas for the proof of our theorem.
Lemma 1 ()
Lemma 2 ()
4 Proof of the theorem
This completes the proof of the theorem. If we take and , then we get a result for summability factors. Also, if we take , , and , then we get a result for summability.
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