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

Year 2019, Volume: 23 Issue: 4, 515 - 518, 01.08.2019
https://doi.org/10.16984/saufenbilder.486492

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  $l(\mu)$.





References

  • [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.
Year 2019, Volume: 23 Issue: 4, 515 - 518, 01.08.2019
https://doi.org/10.16984/saufenbilder.486492

Abstract

References

  • [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.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Fadime Gökçe 0000-0003-1819-3317

Publication Date August 1, 2019
Submission Date November 21, 2018
Acceptance Date December 11, 2018
Published in Issue Year 2019 Volume: 23 Issue: 4

Cite

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