Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 11 Sayı: 3, 182 - 189, 31.12.2022
https://doi.org/10.54187/jnrs.1172611

Öz

Kaynakça

  • T. M. Flett, On an extension of absolute summability and theorems of Littlewood and Paley, Proceedings of the London Mathematical Society, s3-7(1), (1957) 113-141.
  • F. Gökçe, M. A. Sarıgöl, Series spaces derived from absolute Fibonacci summability and matrix transformations, Bollettino dell'Unione Matematica Italiana, 13(1), (2020) 29-38.
  • F. Gökçe, M. A. Sarıgöl, On absolute Euler spaces and related matrix operators, Proceedings of the National Academy of Sciences, India Section A Physical Sciences, 90(5), (2020) 769-775.
  • F. Gökçe, G. C. H. Güleç, Compact and matrix operators on the space $\left\vert A_{f}^{\theta}\right\vert _{k}$, Tbilisi Mathematical Journal, 12(4), (2019) 1-13.
  • F. Gökçe, M. A. Sarıgöl, Generalization of the space $l(p)$ derived by absolute Euler summability and matrix operators, Journal of Inequalities and Applications, 2018, (2018) Article No: 133, 1-10.
  • F. Gökçe, M. A. Sarıgöl, A new series space $\left\vert \overline{N}_{p}^{\theta }\right\vert\left( \mu \right) $ and matrix transformations with applications, Kuwait Journal of Science, 45(4), (2018) 1-8.
  • G. C. Hazar, F. Gökçe, On summability methods $\left\vert A_f \right\vert_k$ and $\left\vert C, 0\right\vert_s$, Bulletin of Mathematical Analysis and Applications, 8(1), (2016) 22-26.
  • M. Ilkhan, Matrix domain of a regular matrix derived by Euler Totient function in the spaces $c_0$ and $c$, Mediterranean Journal of Mathematics, 17(1), (2020) 1-21.
  • M. A. Sarıgöl, On absolute factorable matrix summability methods, Bulletin of Mathematical Analysis and Applications, 8(1), (2016) 1-5.
  • M. A. Sarıgöl, On absolute double summability methods with high indices, Mathematica Slovaca, 71(6), (2021) 1471-1476.
  • M. A. Sarıgöl, On equivalence of absolute double weighted mean methods, Quaestiones Mathematicae, 44(6), (2021) 755-764.
  • B. E. Rhoades, Absolute comparison theorems for double weighted mean and double Ces$\grave{a}$ro means, Mathematica Slovaca, 48(3), (1998) 285-301.
  • B. E. Rhoades, On absolute normal double matrix summability methods, Glasnik Matematicki, 38(58), (2003) 57-73.
  • M. A. Sarıgöl, Four dimensional matrix mappings and applications, Kuwait Journal of Science, (2022) In Press.
  • B. Altay, F. Başar, Some new spaces of double sequences, Journal of Mathematical Analysis and Applications, 309(1), (2005) 70-90.
  • F. Başar, Y. Sever, The space $\mathcal{L}_{q}$ of double sequences, Mathematical Journal of Okayama University, 51(1), (2009) 149-157. M. Zeltser, Investigation of double sequence spaces by soft and hard analytical methods, Tartu University Press, Tartu, 2001.

On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$

Yıl 2022, Cilt: 11 Sayı: 3, 182 - 189, 31.12.2022
https://doi.org/10.54187/jnrs.1172611

Öz

Recently, for single series, the necessary and sufficient conditions for $\left\vert C,0\right\vert\Rightarrow \left\vert A_{f}\right\vert_{k}$ and vise versa, and $\left\vert A_{f}\right\vert \Rightarrow \left\vert C,0\right\vert_{k}$ and vise versa have been established, where $1 < k < \infty $ and $A$ is a factorable matrix. The present study extends these results to double summability, and also provides some new results.

Kaynakça

  • T. M. Flett, On an extension of absolute summability and theorems of Littlewood and Paley, Proceedings of the London Mathematical Society, s3-7(1), (1957) 113-141.
  • F. Gökçe, M. A. Sarıgöl, Series spaces derived from absolute Fibonacci summability and matrix transformations, Bollettino dell'Unione Matematica Italiana, 13(1), (2020) 29-38.
  • F. Gökçe, M. A. Sarıgöl, On absolute Euler spaces and related matrix operators, Proceedings of the National Academy of Sciences, India Section A Physical Sciences, 90(5), (2020) 769-775.
  • F. Gökçe, G. C. H. Güleç, Compact and matrix operators on the space $\left\vert A_{f}^{\theta}\right\vert _{k}$, Tbilisi Mathematical Journal, 12(4), (2019) 1-13.
  • F. Gökçe, M. A. Sarıgöl, Generalization of the space $l(p)$ derived by absolute Euler summability and matrix operators, Journal of Inequalities and Applications, 2018, (2018) Article No: 133, 1-10.
  • F. Gökçe, M. A. Sarıgöl, A new series space $\left\vert \overline{N}_{p}^{\theta }\right\vert\left( \mu \right) $ and matrix transformations with applications, Kuwait Journal of Science, 45(4), (2018) 1-8.
  • G. C. Hazar, F. Gökçe, On summability methods $\left\vert A_f \right\vert_k$ and $\left\vert C, 0\right\vert_s$, Bulletin of Mathematical Analysis and Applications, 8(1), (2016) 22-26.
  • M. Ilkhan, Matrix domain of a regular matrix derived by Euler Totient function in the spaces $c_0$ and $c$, Mediterranean Journal of Mathematics, 17(1), (2020) 1-21.
  • M. A. Sarıgöl, On absolute factorable matrix summability methods, Bulletin of Mathematical Analysis and Applications, 8(1), (2016) 1-5.
  • M. A. Sarıgöl, On absolute double summability methods with high indices, Mathematica Slovaca, 71(6), (2021) 1471-1476.
  • M. A. Sarıgöl, On equivalence of absolute double weighted mean methods, Quaestiones Mathematicae, 44(6), (2021) 755-764.
  • B. E. Rhoades, Absolute comparison theorems for double weighted mean and double Ces$\grave{a}$ro means, Mathematica Slovaca, 48(3), (1998) 285-301.
  • B. E. Rhoades, On absolute normal double matrix summability methods, Glasnik Matematicki, 38(58), (2003) 57-73.
  • M. A. Sarıgöl, Four dimensional matrix mappings and applications, Kuwait Journal of Science, (2022) In Press.
  • B. Altay, F. Başar, Some new spaces of double sequences, Journal of Mathematical Analysis and Applications, 309(1), (2005) 70-90.
  • F. Başar, Y. Sever, The space $\mathcal{L}_{q}$ of double sequences, Mathematical Journal of Okayama University, 51(1), (2009) 149-157. M. Zeltser, Investigation of double sequence spaces by soft and hard analytical methods, Tartu University Press, Tartu, 2001.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Fadime Gökçe 0000-0003-1819-3317

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 11 Sayı: 3

Kaynak Göster

APA Gökçe, F. (2022). On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$. Journal of New Results in Science, 11(3), 182-189. https://doi.org/10.54187/jnrs.1172611
AMA Gökçe F. On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$. JNRS. Aralık 2022;11(3):182-189. doi:10.54187/jnrs.1172611
Chicago Gökçe, Fadime. “On Double Summability Methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$”. Journal of New Results in Science 11, sy. 3 (Aralık 2022): 182-89. https://doi.org/10.54187/jnrs.1172611.
EndNote Gökçe F (01 Aralık 2022) On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$. Journal of New Results in Science 11 3 182–189.
IEEE F. Gökçe, “On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$”, JNRS, c. 11, sy. 3, ss. 182–189, 2022, doi: 10.54187/jnrs.1172611.
ISNAD Gökçe, Fadime. “On Double Summability Methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$”. Journal of New Results in Science 11/3 (Aralık 2022), 182-189. https://doi.org/10.54187/jnrs.1172611.
JAMA Gökçe F. On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$. JNRS. 2022;11:182–189.
MLA Gökçe, Fadime. “On Double Summability Methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$”. Journal of New Results in Science, c. 11, sy. 3, 2022, ss. 182-9, doi:10.54187/jnrs.1172611.
Vancouver Gökçe F. On double summability methods $\left| \mathcal{A}_{f}\right| _{k}$ and $\left| C,0,0\right|_{s}$. JNRS. 2022;11(3):182-9.


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