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Vector-valued Cesàro summable generalized Lorentz sequence space

Year 2017, Volume: 66 Issue: 1, 179 - 186, 01.02.2017
https://doi.org/10.1501/Commua1_0000000787

Abstract

The main purpose of this paper is to introduce Cesàro summable generalized Lorentz sequence space C1[d(v; p)]. We study some topologicproperties of this space and obtain some inclusion relations

References

  • Cui Y. A., Hudzik H., Some Geometric Properties Related to Fixed Point Theory in Cesàro Spaces, Collect. Math., 50 (3) (1999), 277-288.
  • Hardy G. H., Littlewood J. E., Pólya G., Inequalities, Cambridge Univ. Press, 1967.
  • Kato M., On Lorentz Spaces lp;qfEg, Hiroshima Math. J., 6 (1976), 73-93
  • Kızmaz H., On Certain Sequence Spaces, Canad. Math. Bull., Vol. 24 (2), 1981.
  • Lee P. Y., Cesàro Sequence Space, Math. Chronicle, 13 (1984),29-45.
  • Lorentz G. G., Some New Functional Spaces, Ann. Math., 51 (1950), 37-55.
  • Lorentz G. G., On the Theory of Spaces Maddox I. J., Elements of Functional Analysis, Cambridge Univ. Press, 1970.
  • Miyazaki K., (p; q) Nuclear and (p; q) Integral Operators, Hiroshima Math. J., 4(1974), , Pasi…c J. Math., 1 (1951), 411-429. 132.
  • Nawrocki M., Ortynski A., The Mackey Topology and Complemented Subspaces of Lorentz Sequence Spaces d(w; p) for 0 < p < 1, Trans. Amer. Math. Soc., 287 (1985).
  • Petrot N., Suantai S., On Uniform Kadec-Klee Properties and Rodundity in Generalized Cesàro Sequence Spaces, Internat. J. Math. Sci., 2 (2004), 91-97.
  • Popa N., Basic Sequences and Subspaces in Lorentz Sequence Spaces Without Local Convex- ity, Trans. Amer. Math. Soc., 263 (1981), 431-456.
  • Sanhan W., Suantai S., On k nearly Uniform Convex Properties in Generalized Cesàro Sequence Spaces, Internat. J. Math. Sci., 57 (2003), 3599-3607.
  • Shiue J. S., On the Cesàro Sequence Spaces, Tamkang J. Math., 1 (1970), 19-25.
Year 2017, Volume: 66 Issue: 1, 179 - 186, 01.02.2017
https://doi.org/10.1501/Commua1_0000000787

Abstract

References

  • Cui Y. A., Hudzik H., Some Geometric Properties Related to Fixed Point Theory in Cesàro Spaces, Collect. Math., 50 (3) (1999), 277-288.
  • Hardy G. H., Littlewood J. E., Pólya G., Inequalities, Cambridge Univ. Press, 1967.
  • Kato M., On Lorentz Spaces lp;qfEg, Hiroshima Math. J., 6 (1976), 73-93
  • Kızmaz H., On Certain Sequence Spaces, Canad. Math. Bull., Vol. 24 (2), 1981.
  • Lee P. Y., Cesàro Sequence Space, Math. Chronicle, 13 (1984),29-45.
  • Lorentz G. G., Some New Functional Spaces, Ann. Math., 51 (1950), 37-55.
  • Lorentz G. G., On the Theory of Spaces Maddox I. J., Elements of Functional Analysis, Cambridge Univ. Press, 1970.
  • Miyazaki K., (p; q) Nuclear and (p; q) Integral Operators, Hiroshima Math. J., 4(1974), , Pasi…c J. Math., 1 (1951), 411-429. 132.
  • Nawrocki M., Ortynski A., The Mackey Topology and Complemented Subspaces of Lorentz Sequence Spaces d(w; p) for 0 < p < 1, Trans. Amer. Math. Soc., 287 (1985).
  • Petrot N., Suantai S., On Uniform Kadec-Klee Properties and Rodundity in Generalized Cesàro Sequence Spaces, Internat. J. Math. Sci., 2 (2004), 91-97.
  • Popa N., Basic Sequences and Subspaces in Lorentz Sequence Spaces Without Local Convex- ity, Trans. Amer. Math. Soc., 263 (1981), 431-456.
  • Sanhan W., Suantai S., On k nearly Uniform Convex Properties in Generalized Cesàro Sequence Spaces, Internat. J. Math. Sci., 57 (2003), 3599-3607.
  • Shiue J. S., On the Cesàro Sequence Spaces, Tamkang J. Math., 1 (1970), 19-25.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Oğuz Oğur This is me

Birsen Sağır This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Oğur, O., & Sağır, B. (2017). Vector-valued Cesàro summable generalized Lorentz sequence space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 179-186. https://doi.org/10.1501/Commua1_0000000787
AMA Oğur O, Sağır B. Vector-valued Cesàro summable generalized Lorentz sequence space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):179-186. doi:10.1501/Commua1_0000000787
Chicago Oğur, Oğuz, and Birsen Sağır. “Vector-Valued Cesàro Summable Generalized Lorentz Sequence Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 179-86. https://doi.org/10.1501/Commua1_0000000787.
EndNote Oğur O, Sağır B (February 1, 2017) Vector-valued Cesàro summable generalized Lorentz sequence space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 179–186.
IEEE O. Oğur and B. Sağır, “Vector-valued Cesàro summable generalized Lorentz sequence space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 179–186, 2017, doi: 10.1501/Commua1_0000000787.
ISNAD Oğur, Oğuz - Sağır, Birsen. “Vector-Valued Cesàro Summable Generalized Lorentz Sequence Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 179-186. https://doi.org/10.1501/Commua1_0000000787.
JAMA Oğur O, Sağır B. Vector-valued Cesàro summable generalized Lorentz sequence space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:179–186.
MLA Oğur, Oğuz and Birsen Sağır. “Vector-Valued Cesàro Summable Generalized Lorentz Sequence Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 179-86, doi:10.1501/Commua1_0000000787.
Vancouver Oğur O, Sağır B. Vector-valued Cesàro summable generalized Lorentz sequence space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):179-86.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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