Research Article
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On some new sequence spaces

Year 2018, Volume: 20 Issue: 3, 154 - 162, 29.10.2018
https://doi.org/10.25092/baunfbed.487747
https://izlik.org/JA96MD78JY

Abstract

In this paper, we investigate some new sequence spaces which arise from the notation of generalized de la Vallée-Poussin means and introduce the spaces of strongly λ- invariant summable sequences which happen to be complete paranormed spaces under certain conditions.

References

  • Banach, S., Theorie des Operations Lineaires, (1932).
  • Duran, J.P., Infinite matrices and almost convergence, Math. Z., 128, 75-83, (1972).
  • Hamilton, H.J. and Hill, J. D., On strong summability, Amer. J. Math., 60, 588-94, (1938).
  • Kuttner, B., Note on strong summability, J. London Math. Soc., 21, 118-22, (1946).
  • King, J.P., Almost summable sequences, Proc. Amer. Math. Soc., 17, 1219-25, (1966).
  • Lorentz, G.G., A contribution to the theory of divergent sequences, Acta Math., 80, 167-190, (1948).
  • Maddox, I.J., Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser., (2)18, 345-55, (1967).
  • Maddox, I.J., Elements of Functional Analysis, Cambridge University Press, (1970).
  • Malkowsky, E. and Savaş, E., Some -sequence spaces defined by a modulus, Archivum Math., 36(3), 219-228, (2000).
  • Mursaleen, M., Matrix transformation between some new sequence spaces, Houston J. Math., 9, 505–509, (1993),.
  • Mursaleen, M., On some new invariant matrix methods of summability, Q.J. Math., 34, 77-86, (1983).
  • Nanda, S., Some sequence spaces and almost convergence, J. Austral. Math. Soc. (Series A), 22, 446-455, (1976).
  • Savaş, E., Some sequence spaces involving invariant means, Indian J. Math., 31, (1989).
  • Savaş, E., A note on some sequence spaces, Doğa Türk. J. Math., 15, (1991).
  • Savaş, E., Invariant means and generalization of a theorem of S. Mishra, Doga Türk. J. Math., 14, (1989).
  • Savaş, E., Invariant coregular and conull matrices of operators, Hacettepe Bull. Math. Sci. and Eng., 19, (1990).
  • Savaş, E., Infinite matrices and generalized almost convergence, Doga Türk. J. Math., 5(3), 1-10, (1987).
  • Saraswat, S.K. and Gupta, S.K., Spaces of strongly -summable sequences, Bull. Cal. Math. Soc., 75, 179-184, (1983).
  • Schaefer, P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36, 104–110, (1972).

Bazı yeni dizi uzayları üzerine

Year 2018, Volume: 20 Issue: 3, 154 - 162, 29.10.2018
https://doi.org/10.25092/baunfbed.487747
https://izlik.org/JA96MD78JY

Abstract

Bu makalede, genelleştirilmiş de la Vallée-Poussin ortalamalarından ortaya çıkan bazı yeni dizi uzayları incelenmiş ve belirli koşullar altında tam paranormlu uzay olan kuvvetli λ-değişmez toplanabilir dizi uzayları tanıtılmıştır.

References

  • Banach, S., Theorie des Operations Lineaires, (1932).
  • Duran, J.P., Infinite matrices and almost convergence, Math. Z., 128, 75-83, (1972).
  • Hamilton, H.J. and Hill, J. D., On strong summability, Amer. J. Math., 60, 588-94, (1938).
  • Kuttner, B., Note on strong summability, J. London Math. Soc., 21, 118-22, (1946).
  • King, J.P., Almost summable sequences, Proc. Amer. Math. Soc., 17, 1219-25, (1966).
  • Lorentz, G.G., A contribution to the theory of divergent sequences, Acta Math., 80, 167-190, (1948).
  • Maddox, I.J., Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser., (2)18, 345-55, (1967).
  • Maddox, I.J., Elements of Functional Analysis, Cambridge University Press, (1970).
  • Malkowsky, E. and Savaş, E., Some -sequence spaces defined by a modulus, Archivum Math., 36(3), 219-228, (2000).
  • Mursaleen, M., Matrix transformation between some new sequence spaces, Houston J. Math., 9, 505–509, (1993),.
  • Mursaleen, M., On some new invariant matrix methods of summability, Q.J. Math., 34, 77-86, (1983).
  • Nanda, S., Some sequence spaces and almost convergence, J. Austral. Math. Soc. (Series A), 22, 446-455, (1976).
  • Savaş, E., Some sequence spaces involving invariant means, Indian J. Math., 31, (1989).
  • Savaş, E., A note on some sequence spaces, Doğa Türk. J. Math., 15, (1991).
  • Savaş, E., Invariant means and generalization of a theorem of S. Mishra, Doga Türk. J. Math., 14, (1989).
  • Savaş, E., Invariant coregular and conull matrices of operators, Hacettepe Bull. Math. Sci. and Eng., 19, (1990).
  • Savaş, E., Infinite matrices and generalized almost convergence, Doga Türk. J. Math., 5(3), 1-10, (1987).
  • Saraswat, S.K. and Gupta, S.K., Spaces of strongly -summable sequences, Bull. Cal. Math. Soc., 75, 179-184, (1983).
  • Schaefer, P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36, 104–110, (1972).
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ekrem Savaş

Submission Date November 4, 2018
Publication Date October 29, 2018
DOI https://doi.org/10.25092/baunfbed.487747
IZ https://izlik.org/JA96MD78JY
Published in Issue Year 2018 Volume: 20 Issue: 3

Cite

APA Savaş, E. (2018). On some new sequence spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 154-162. https://doi.org/10.25092/baunfbed.487747
AMA 1.Savaş E. On some new sequence spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2018;20(3):154-162. doi:10.25092/baunfbed.487747
Chicago Savaş, Ekrem. 2018. “On Some New Sequence Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (3): 154-62. https://doi.org/10.25092/baunfbed.487747.
EndNote Savaş E (October 1, 2018) On some new sequence spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 3 154–162.
IEEE [1]E. Savaş, “On some new sequence spaces”, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 3, pp. 154–162, Oct. 2018, doi: 10.25092/baunfbed.487747.
ISNAD Savaş, Ekrem. “On Some New Sequence Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/3 (October 1, 2018): 154-162. https://doi.org/10.25092/baunfbed.487747.
JAMA 1.Savaş E. On some new sequence spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2018;20:154–162.
MLA Savaş, Ekrem. “On Some New Sequence Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 3, Oct. 2018, pp. 154-62, doi:10.25092/baunfbed.487747.
Vancouver 1.Ekrem Savaş. On some new sequence spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2018 Oct. 1;20(3):154-62. doi:10.25092/baunfbed.487747