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.

scholarly journals On inclusion relations for absolute summability

2002 ◽  
Vol 32 (3) ◽  
pp. 129-138 ◽  
Author(s):  
B. E. Rhoades ◽  
Ekrem Savaş
Keyword(s):  
Sufficient Conditions ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Lower Triangular Matrix ◽  
Weighted Mean ◽  
Inclusion Relations ◽  
Lower Triangular

We obtain necessary and (different) sufficient conditions for a series summable|N¯,pn|k,1<k≤s<∞, to imply that the series is summable|T|s, where(N¯,pn)is a weighted mean matrix andTis a lower triangular matrix. As corollaries of this result, we obtain several inclusion theorems.

scholarly journals New results for almost increasing sequences

2019 ◽  
Vol 18 (1) ◽  
pp. 85-91
Author(s):  
Bağdagül Kartal
Keyword(s):  
Absolute Summability ◽  
Definition Of ◽  
Increasing Sequences ◽  
Almost Increasing Sequences

Abstract In the present paper, two theorems of absolute summability have been proved by using the definition of almost increasing sequence.

A new factor theorem on absolute matrix summability method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Şebnem Yıldız
Keyword(s):  
Infinite Series ◽  
Summability Method ◽  
Summability Factor ◽  
Matrix Summability ◽  
Absolute Matrix Summability ◽  
Matrix Generalization ◽  
Summability Methods ◽  
Power Increasing Sequences ◽  
Factor Theorem ◽  
Increasing Sequences

Abstract In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods

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