On two absolute Riesz summability factors of infinite series

Sarigöl, Mehmet Ali

doi:10.1090/s0002-9939-1993-1127143-8

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G Canan Hazar Güleç and Mehmet Ali Sarigöl1

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Cited by 11 publications

(6 citation statements)

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“…The summability | , , | includes all Cesàro methods in the special cases. For example, if we take = 0, = 0 and = 1, then the summability | , , | reduces to | , | defined by Flett in [7], to | , 0| and the absolute Riesz summability | , | with = for ≥ 0 [3].…”

Section: =1mentioning

confidence: 99%

A study on absolute summability factors

Güleç

2020

Sakarya University Journal of Science

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Section: =1mentioning

confidence: 99%

A study on absolute summability factors

Güleç

2020

Sakarya University Journal of Science

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“…If Σǫ n a n is summable Y whenever Σa n is summable X , then ǫ is said to be a summability factor of type (X , Y ) and we denote it by ǫ ∈ (X , Y ) [3] . The problems of summability factors dealing with absolute Cesàro and absolute weighted mean summabilities were widely examined by many authors (see [1][2][3][4] , [8][9][10][11] , [13][14][15][16][17][18][19][20][21]…”

Section: G Canan Hazar Güleç and Mehmet Ali Sarigölmentioning

confidence: 99%

On factor relations between weighted and Nörlund means

Güleç

Sarigöl

2018

Tamkang J. Math.

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By $\left( X,Y\right) ,$ we denote the set of all sequences $\epsilon =\left( \epsilon _{n}\right) $ such that $\Sigma \epsilon _{n}a_{n}$ is summable $Y$ whenever $\Sigma a_{n}$ is summable $X,$ where $X$ and $Y$ are two summability methods. In this study, we get necessary and sufficient conditions for $\epsilon \in \left( \left\vert N,q_{n},u_{n}\right\vert _{k},\left\vert \bar{N},p_{n}\right\vert \right) $ and $\epsilon \in \left( \left\vert \bar{N},p_{n}\right\vert ,\left\vert N,q_{n},u_{n}\right\vert _{k}\right) $, $k\geq 1,$ using functional analytic tecniques, where $% \left\vert \bar{N},p_{n}\right\vert $ and $\left\vert N,q_{n},u_{n}\right\vert _{k}$ are absolute weighted and N\"{o}rlund summability methods, respectively, \cite{1}, \cite{5}. Thus, in the special case, some well known results are also deduced.

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“…We can write |R, λ n , 1| for |N , p n |, where P n = λ n , and 0 < λ 1 < ... < λ n → ∞, n → ∞. Many studies have been done for absolute summability factors of infinite series and Fourier series by using different summability methods (see [1]- [2], [6], [8]- [11], [13]- [17]). Furthermore, in this paper, we obtained new generalizations of absolute summability factors of Fourier series and its conjugate series.…”

Section: Introductionmentioning

confidence: 99%