Araştırma Makalesi
BibTex RIS Kaynak Göster

On some Zweier convergent vector valued multiplier spaces

Yıl 2019, Cilt: 23 Sayı: 4, 541 - 548, 01.08.2019
https://doi.org/10.16984/saufenbilder.492788

Öz



In this
paper, we introduce the Zweier convergent vector valued multiplier spaces
M^\infty_Z(\sum_iT_ix_i)



















and M^\infty_wZ(\sum_iT_ix_i). We examine some topological
properties and some inclusion relations of these spaces.



Kaynakça

  • A. Aizpuru, C. Pérez-Eslava, and J. B. Seoane Sepúlveda, “Matrix summability methods and weakly unconditionally Cauchy series,” The Rocky Mountain Journal of Mathematics, vol. 39, no. 2, pp. 367-380, 2009.
  • F. Albiac and N. J. Kalton, “Topics in Banach Spaces Theory,” New York, Springer-Verlag, 2006.
  • B. Altay and R. Kama, “On Cesàro summability of vector valued multiplier spaces and operator valued series,” Positivity, vol. 22, no. 2, pp. 575-586, 2018.
  • F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers, İstanbul, 2012.
  • F. Başar and B. Altay, “On the space of sequences of p-bounded variation and related matrix mappings”, (English, Ukrainian summary) Ukrain. Mat. Zh., vol. 55, no. 1, pp. 108-118, 2003; reprinted in Ukrainian Math. J., vol. 55, no. 1, pp. 136-14, 2003.
  • J. Boos and P. Cass, “Classical and Modern Methods in Summability,” Oxford University Press, Oxford, 2000.
  • J. Diestel, “Sequences and Series in Banach Spaces,” New York, Springer-Verlag, 1984.
  • B. Hazarika, T. Karan, and B. K. Singh, “Zweier Ideal convergent sequence space defined by Orlicz function,” Journal of mathematics and computer science, vol. 8, no. 3, pp. 307-318, 2014.
  • V. A. Khan, K. Ebadullah, A. Esi, and M. Shafiq, “On some Zweier I-convergent sequence spaces defined by a modulus function,” Afrika Matematika, vol. 26, no. 1-2, pp. 115-125, 2015.
  • V. A. Khan and N. Khan, “Zweier I-Convergent Double Sequence Spaces Defined by a Sequence of Moduli,” Theory and Applications of Mathematics and Computer Science, vol. 5, no. 2, pp. 194-202, 2015.
  • M. Mursaleen, “Applied Summability Methods, Springer Briefs,” Heidelberg New York Dordrecht London, 2014.
  • F. J. Pérez-Fernández, F. Benítez-Trujillo, and A. Aizpuru, “Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series,” Czechoslovak Math. J., vol. 50, no. 4, pp. 889-896, 2000.
  • C. Swartz, “Multiplier Convergent Series,” Singapore, World Sci. Publ., 2009.
  • C. Swartz, “Operator valued series and vector valued multiplier spaces,” Casp. J. Math. Sci., vol. 3, no. 2, pp. 277-288, 2014.
  • M. Şengönül, “On the Zweier sequence space,” Demonstratio Mathematica, vol. 40, no. 1, pp. 181-196, 2007.
Yıl 2019, Cilt: 23 Sayı: 4, 541 - 548, 01.08.2019
https://doi.org/10.16984/saufenbilder.492788

Öz

Kaynakça

  • A. Aizpuru, C. Pérez-Eslava, and J. B. Seoane Sepúlveda, “Matrix summability methods and weakly unconditionally Cauchy series,” The Rocky Mountain Journal of Mathematics, vol. 39, no. 2, pp. 367-380, 2009.
  • F. Albiac and N. J. Kalton, “Topics in Banach Spaces Theory,” New York, Springer-Verlag, 2006.
  • B. Altay and R. Kama, “On Cesàro summability of vector valued multiplier spaces and operator valued series,” Positivity, vol. 22, no. 2, pp. 575-586, 2018.
  • F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers, İstanbul, 2012.
  • F. Başar and B. Altay, “On the space of sequences of p-bounded variation and related matrix mappings”, (English, Ukrainian summary) Ukrain. Mat. Zh., vol. 55, no. 1, pp. 108-118, 2003; reprinted in Ukrainian Math. J., vol. 55, no. 1, pp. 136-14, 2003.
  • J. Boos and P. Cass, “Classical and Modern Methods in Summability,” Oxford University Press, Oxford, 2000.
  • J. Diestel, “Sequences and Series in Banach Spaces,” New York, Springer-Verlag, 1984.
  • B. Hazarika, T. Karan, and B. K. Singh, “Zweier Ideal convergent sequence space defined by Orlicz function,” Journal of mathematics and computer science, vol. 8, no. 3, pp. 307-318, 2014.
  • V. A. Khan, K. Ebadullah, A. Esi, and M. Shafiq, “On some Zweier I-convergent sequence spaces defined by a modulus function,” Afrika Matematika, vol. 26, no. 1-2, pp. 115-125, 2015.
  • V. A. Khan and N. Khan, “Zweier I-Convergent Double Sequence Spaces Defined by a Sequence of Moduli,” Theory and Applications of Mathematics and Computer Science, vol. 5, no. 2, pp. 194-202, 2015.
  • M. Mursaleen, “Applied Summability Methods, Springer Briefs,” Heidelberg New York Dordrecht London, 2014.
  • F. J. Pérez-Fernández, F. Benítez-Trujillo, and A. Aizpuru, “Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series,” Czechoslovak Math. J., vol. 50, no. 4, pp. 889-896, 2000.
  • C. Swartz, “Multiplier Convergent Series,” Singapore, World Sci. Publ., 2009.
  • C. Swartz, “Operator valued series and vector valued multiplier spaces,” Casp. J. Math. Sci., vol. 3, no. 2, pp. 277-288, 2014.
  • M. Şengönül, “On the Zweier sequence space,” Demonstratio Mathematica, vol. 40, no. 1, pp. 181-196, 2007.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Ramazan Kama 0000-0003-3520-1227

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 6 Aralık 2018
Kabul Tarihi 31 Aralık 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 23 Sayı: 4

Kaynak Göster

APA Kama, R. (2019). On some Zweier convergent vector valued multiplier spaces. Sakarya University Journal of Science, 23(4), 541-548. https://doi.org/10.16984/saufenbilder.492788
AMA Kama R. On some Zweier convergent vector valued multiplier spaces. SAUJS. Ağustos 2019;23(4):541-548. doi:10.16984/saufenbilder.492788
Chicago Kama, Ramazan. “On Some Zweier Convergent Vector Valued Multiplier Spaces”. Sakarya University Journal of Science 23, sy. 4 (Ağustos 2019): 541-48. https://doi.org/10.16984/saufenbilder.492788.
EndNote Kama R (01 Ağustos 2019) On some Zweier convergent vector valued multiplier spaces. Sakarya University Journal of Science 23 4 541–548.
IEEE R. Kama, “On some Zweier convergent vector valued multiplier spaces”, SAUJS, c. 23, sy. 4, ss. 541–548, 2019, doi: 10.16984/saufenbilder.492788.
ISNAD Kama, Ramazan. “On Some Zweier Convergent Vector Valued Multiplier Spaces”. Sakarya University Journal of Science 23/4 (Ağustos 2019), 541-548. https://doi.org/10.16984/saufenbilder.492788.
JAMA Kama R. On some Zweier convergent vector valued multiplier spaces. SAUJS. 2019;23:541–548.
MLA Kama, Ramazan. “On Some Zweier Convergent Vector Valued Multiplier Spaces”. Sakarya University Journal of Science, c. 23, sy. 4, 2019, ss. 541-8, doi:10.16984/saufenbilder.492788.
Vancouver Kama R. On some Zweier convergent vector valued multiplier spaces. SAUJS. 2019;23(4):541-8.

Cited By

Sakarya University Journal of Science (SAUJS)