Year 2019, Volume 23 , Issue 4, Pages 515 - 518 2019-08-01

A Note On The Series Space |N ̅_p^θ |(μ)

Fadime Gökçe [1]


The series space $\left\vert \bar{N}_{p}^{\theta }\right\vert\left( \mu \right) $ has recently been introduced and studied by Gökçe and Sarıgöl [1]. The main purpose of this paper is to determine the  $\alpha-$$\beta-$  and  $\gamma$_duals of the space  and to show that it is linearly isomorphic to the Maddox’s space  $l(\mu)$.





Absolute summability, Sequence spaces, Weighted mean, Duals, Isomorphism
  • [1] F. Gökçe and M.A. Sarıgöl, “A new series space |N ̅_p^θ |(μ) and matrix operatör with applications”, Kuwait Journal of Science, vol. 45, no. 4, pp. 1-8, 2018.[2] I.J.. Maddox,, “Some properties of paranormed sequence spaces,” Journal of the London Mathematical Society, vol. 1, pp. 316–322, 1969.[3] I.J.. Maddox, “Paranormed sequence spaces Generated by infinite matrices,”Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335–340, 1968.[4] I.J. Maddox, “Spaces of strongly summable sequences,” The Quarterly Journal of Mathematics, vol. 18, pp. 345–355, 1967.[5] H. Bor, “On |N ̅,p_n |_k summability factors of infinite series,” Tamkang J. Math, vol. 16, no. 1, pp. 13– 20, 1985.[6] T.M. FLett,, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. London Math. Soc., vol. 7, pp. 113-141, 1957.[7] M.A. Sarıgöl, “Spaces of series summable by absolute Cesàro and matrix operators,” Comm. Math. Appl., vol. 7, pp. 11–22, 2016.[8] M.A. Sarıgöl, “Norms and compactness of operators on absolute weighted mean, summable series,” Kuwait Journal of Science, vol. 43, no. 4, pp. 68–74, 2016.[9] M.A. Sarıgöl, “An inequality for matrix operators and its applications.,” J. Classical Anal, vol. 2, pp. 145–150, 2013. [10] M.A. Sarıgöl, “Matrix transformations on fields of absolute weighted mean summability,” Studia Scientiarum Mathematicarum Hungarica., vol. 48, no. 3, pp. 331–341, 2011.[11] M.A. Sarıgöl, “On local properties of factored Fourier series.,” Appl. Math. Comp., vol. 216, no. 3, pp. 3386–3390, 2010.[12] K.G. Grosse-Erdmann,, “Matrix transformations between the sequence spaces of Maddox.,” Journal of Mathematical Analysis and Applications, vol. 180, pp. 223–238, 1993.
Primary Language en
Subjects Mathematics
Published Date August 2019
Journal Section Research Articles
Authors

Orcid: 0000-0003-1819-3317
Author: Fadime Gökçe (Primary Author)
Institution: PAMUKKALE UNIVERSITY
Country: Turkey


Dates

Application Date : November 21, 2018
Acceptance Date : December 11, 2018
Publication Date : August 1, 2019

Bibtex @research article { saufenbilder486492, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2019}, volume = {23}, pages = {515 - 518}, doi = {10.16984/saufenbilder.486492}, title = {A Note On The Series Space |N ̅\_p\^θ |(μ)}, key = {cite}, author = {Gökçe, Fadime} }
APA Gökçe, F . (2019). A Note On The Series Space |N ̅_p^θ |(μ). Sakarya University Journal of Science , 23 (4) , 515-518 . DOI: 10.16984/saufenbilder.486492
MLA Gökçe, F . "A Note On The Series Space |N ̅_p^θ |(μ)". Sakarya University Journal of Science 23 (2019 ): 515-518 <http://www.saujs.sakarya.edu.tr/en/issue/43328/486492>
Chicago Gökçe, F . "A Note On The Series Space |N ̅_p^θ |(μ)". Sakarya University Journal of Science 23 (2019 ): 515-518
RIS TY - JOUR T1 - A Note On The Series Space |N ̅_p^θ |(μ) AU - Fadime Gökçe Y1 - 2019 PY - 2019 N1 - doi: 10.16984/saufenbilder.486492 DO - 10.16984/saufenbilder.486492 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 515 EP - 518 VL - 23 IS - 4 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.486492 UR - https://doi.org/10.16984/saufenbilder.486492 Y2 - 2018 ER -
EndNote %0 Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi A Note On The Series Space |N ̅_p^θ |(μ) %A Fadime Gökçe %T A Note On The Series Space |N ̅_p^θ |(μ) %D 2019 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 23 %N 4 %R doi: 10.16984/saufenbilder.486492 %U 10.16984/saufenbilder.486492
ISNAD Gökçe, Fadime . "A Note On The Series Space |N ̅_p^θ |(μ)". Sakarya University Journal of Science 23 / 4 (August 2019): 515-518 . https://doi.org/10.16984/saufenbilder.486492
AMA Gökçe F . A Note On The Series Space |N ̅_p^θ |(μ). SAUJS. 2019; 23(4): 515-518.
Vancouver Gökçe F . A Note On The Series Space |N ̅_p^θ |(μ). Sakarya University Journal of Science. 2019; 23(4): 518-515.