Open Access

Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence

Journal of Inequalities and Applications20082007:081028

Received: 27 August 2007

Accepted: 30 October 2007

Published: 9 January 2008


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.


Authors’ Affiliations

Department of Mathematics, Education Faculty, Adıyaman University


  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/BF01458596MathSciNetView ArticleGoogle Scholar
  2. Chen ST: Geometry of Orlicz spaces. Dissertationes Mathematicae 1996, 356: 204.Google Scholar
  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.MathSciNetMATHGoogle Scholar
  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.MathSciNetMATHGoogle Scholar
  5. Diestel J: Geometry of Banach Spaces-Selected Topics. Springer, Berlin, Germany; 1984.Google Scholar
  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.2004.02.047MathSciNetView ArticleMATHGoogle Scholar
  7. Musielak J: Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics. Volume 1034. Springer, Berlin, Germany; 1983:iii+222.Google Scholar
  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.MathSciNetView ArticleMATHGoogle Scholar
  9. Sanhan W, Suantai S: Some geometric properties of Cesaro sequence space. Kyungpook Mathematical Journal 2003,43(2):191–197.MathSciNetMATHGoogle Scholar
  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.MathSciNetMATHGoogle Scholar
  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/s3-37.3.508MathSciNetView ArticleMATHGoogle Scholar
  12. Das G, Patel BK: Lacunary distribution of sequences. Indian Journal of Pure and Applied Mathematics 1989,20(1):64–74.MathSciNetMATHGoogle Scholar
  13. Fridy JA, Orhan C: Lacunary statistical summability. Journal of Mathematical Analysis and Applications 1993,173(2):497–504. 10.1006/jmaa.1993.1082MathSciNetView ArticleMATHGoogle Scholar
  14. Karakaya V: On lacunary-statistical convergence. Information Sciences 2004,166(1–4):271–280.MathSciNetView ArticleMATHGoogle Scholar
  15. Mursaleen M, Chishti TA: Some spaces of lacunary sequences defined by the modulus. Journal of Analysis 1996, 4: 153–159.MathSciNetMATHGoogle Scholar
  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.MathSciNetMATHGoogle Scholar


© Vatan Karakaya 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.