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

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 Mathematics August 2019 Research Articles Orcid: 0000-0003-1819-3317Author: Fadime GÖKÇE (Primary Author)Institution: PAMUKKALE UNIVERSITYCountry: Turkey 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 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.

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