Research Article

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

Volume: 23 Number: 4 August 1, 2019
EN

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

Abstract

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  $l(\mu)$.





Keywords

References

  1. [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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

August 1, 2019

Submission Date

November 21, 2018

Acceptance Date

December 11, 2018

Published in Issue

Year 2019 Volume: 23 Number: 4

APA
Gökçe, F. (2019). A Note On The Series Space |N ̅_p^θ |(μ). Sakarya University Journal of Science, 23(4), 515-518. https://doi.org/10.16984/saufenbilder.486492
AMA
1.Gökçe F. A Note On The Series Space |N ̅_p^θ |(μ). SAUJS. 2019;23(4):515-518. doi:10.16984/saufenbilder.486492
Chicago
Gökçe, Fadime. 2019. “A Note On The Series Space |N ̅_p^θ |(μ)”. Sakarya University Journal of Science 23 (4): 515-18. https://doi.org/10.16984/saufenbilder.486492.
EndNote
Gökçe F (August 1, 2019) A Note On The Series Space |N ̅_p^θ |(μ). Sakarya University Journal of Science 23 4 515–518.
IEEE
[1]F. Gökçe, “A Note On The Series Space |N ̅_p^θ |(μ)”, SAUJS, vol. 23, no. 4, pp. 515–518, Aug. 2019, doi: 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 1, 2019): 515-518. https://doi.org/10.16984/saufenbilder.486492.
JAMA
1.Gökçe F. A Note On The Series Space |N ̅_p^θ |(μ). SAUJS. 2019;23:515–518.
MLA
Gökçe, Fadime. “A Note On The Series Space |N ̅_p^θ |(μ)”. Sakarya University Journal of Science, vol. 23, no. 4, Aug. 2019, pp. 515-8, doi:10.16984/saufenbilder.486492.
Vancouver
1.Fadime Gökçe. A Note On The Series Space |N ̅_p^θ |(μ). SAUJS. 2019 Aug. 1;23(4):515-8. doi:10.16984/saufenbilder.486492


INDEXING & ABSTRACTING & ARCHIVING

33418 33537  30939     30940 30943 30941  30942  33255    33253  33254

30944  30945  30946   34239




30930Bu eser Creative Commons Atıf-Ticari Olmayan 4.0 Uluslararası Lisans   kapsamında lisanslanmıştır .