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Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence

Abstract

We introduce new sequence space involving lacunary sequence connected with Cesaro sequence space and examine some geometric properties of this space equipped with Luxemburg norm.

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References

  1. 1.

    Lin B-L, Lin P-K, Troyanski SL: Some geometric and topological properties of the unit sphere in Banach spaces. Mathematische Annalen 1986,274(4):613–616. 10.1007/BF01458596

    MathSciNet  Article  Google Scholar 

  2. 2.

    Chen ST: Geometry of Orlicz spaces. Dissertationes Mathematicae 1996, 356: 204.

    Google Scholar 

  3. 3.

    Cui YA, Hudzik H: On the Banach-Saks and weak Banach-Saks properties of some Banach sequence spaces. Acta Scientiarum Mathematicarum 1999,65(1–2):179–187.

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Cui Y, Hudzik H, Nowak M, Płuciennik R: Some geometric properties in Orlicz sequence spaces equipped with Orlicz norm. Journal of Convex Analysis 1999,6(1):91–113.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Diestel J: Geometry of Banach Spaces-Selected Topics. Springer, Berlin, Germany; 1984.

    Google Scholar 

  6. 6.

    Japón MA: Some geometric properties in modular spaces and application to fixed point theory. Journal of Mathematical Analysis and Applications 2004,295(2):576–594. 10.1016/j.jmaa.2004.02.047

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Musielak J: Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics. Volume 1034. Springer, Berlin, Germany; 1983:iii+222.

    Google Scholar 

  8. 8.

    Petrot N, Suantai S: On uniform Kadec-Klee properties and rotundity in generalized Cesàro sequence spaces. International Journal of Mathematics and Mathematical Sciences 2004,2004(1–4):91–97.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Sanhan W, Suantai S: Some geometric properties of Cesaro sequence space. Kyungpook Mathematical Journal 2003,43(2):191–197.

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Sanhan W, Kananthai A, Musarleen M, Suantai S: On property (H) and rotundity of difference sequence spaces. Journal of Nonlinear and Convex Analysis 2002,3(3):401–409.

    MathSciNet  MATH  Google Scholar 

  11. 11.

    Freedman AR, Sember JJ, Raphael M: Some Cesàro-type summability spaces. Proceedings of the London Mathematical Society 1978,37(3):508–520. 10.1112/plms/s3-37.3.508

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Das G, Patel BK: Lacunary distribution of sequences. Indian Journal of Pure and Applied Mathematics 1989,20(1):64–74.

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Fridy JA, Orhan C: Lacunary statistical summability. Journal of Mathematical Analysis and Applications 1993,173(2):497–504. 10.1006/jmaa.1993.1082

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Karakaya V: On lacunary-statistical convergence. Information Sciences 2004,166(1–4):271–280.

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Mursaleen M, Chishti TA: Some spaces of lacunary sequences defined by the modulus. Journal of Analysis 1996, 4: 153–159.

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Pehlivan S, Fisher B: Lacunary strong convergence with respect to a sequence of modulus functions. Commentationes Mathematicae Universitatis Carolinae 1995,36(1):69–76.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Vatan Karakaya.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Karakaya, V. Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence. J Inequal Appl 2007, 081028 (2008). https://doi.org/10.1155/2007/81028

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Keywords

  • Geometric Property
  • Sequence Space
  • Lacunary Sequence
  • Luxemburg Norm
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