Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces

Kama, Ramazan

doi:10.1007/s13398-020-00806-6

Cited by 11 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let D be an infinite matrix of complex entries d nk and x = (x k ) be a complex valued sequence. Then Recently, similar works studied by some authors, see [13][14][15][16][17]. In the present paper, we have proved some Abelian, Tauberian and Core theorems related to the (V, λ )-summability.…”

Section: Preliminariessupporting

confidence: 60%

Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability

Ersoy

2021

Universal Journal of Mathematics and Applications

View full text Add to dashboard Cite

show abstract

Section: Preliminariessupporting

confidence: 60%

Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability

Ersoy

2021

Universal Journal of Mathematics and Applications

View full text Add to dashboard Cite

show abstract

“…There are several results on summability by Nörlund means of Fourier series. The authors [2,4,6,7,9,13,14] have looked into it. This encourages us to research it in both more generalized and particular cases.…”

Section: Resultsmentioning

confidence: 99%

On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)

Sahani¹,

Paudel

Thakur

2022

J. Nep. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…In [20], McArthur investigated some closed linear subspaces of the space of the weakly unconditional summable sequences in a Banach space X and gave some inclusion relations between these spaces. One can refer to the Aizpuru et al [1,3], Pérez-Fernández et al [21], Kama and Altay [10], Kama et al [11], Kama [9,12], Karakuş [13], Karakuş and Başar [14,15,16] and Swartz [22,23] for recent studies on multiplier convergent series.…”

Section: Introductionmentioning

confidence: 99%

Riesz multiplier convergent spaces of operator valued series and a version of Orlicz- Pettis theorem

Karakuş¹,

Kama²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

It is not usual to characterize an operator valued series via completeness of multiplier spaces. In this study, by using a series of bounded linear operators, we introduce the space M ∞ R k T k of Riesz summability which is a generalization of the Cesàro summability. Therefore, we give the completeness criteria of these spaces with c0(X)-multiplier convergent operator series. It is a natural consequence that one can characterize the completeness of a normed space through M ∞ R k T k which will be assumed that is complete for every c0(X)-multiplier Cauchy operator series. Then, we characterize the continuity and the (weakly) compactness of the summing operator S from the multiplier space M ∞ R k T k to an arbitrary normed space Y through c0(X)-multiplier Cauchy and ℓ∞(X)-multiplier convergent series, respectively. We also prove that if k T k is ℓ∞(X)-multiplier Cauchy, then the multiplier space of weakly Riesz-convergence associated to the operator valued seriesAmong other results, finally, we obtain a new version of the well-known Orlicz-Pettis theorem by using Riesz-summability.

show abstract

Spaces of vector sequences defined by the f-statistical convergence and some characterizations of normed spaces

Cited by 11 publications

References 29 publications

Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability

Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability

On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)

Riesz multiplier convergent spaces of operator valued series and a version of Orlicz- Pettis theorem

Contact Info

Product

Resources

About