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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 419560, 6 pages
http://dx.doi.org/10.1155/2014/419560
Research Article

Operator Ideal of Cesaro Type Sequence Spaces Involving Lacunary Sequence

1Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University (KAU), P.O. Box 80200, Khulais 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, Egypt

Received 7 October 2013; Revised 13 January 2014; Accepted 15 January 2014; Published 26 February 2014

Academic Editor: Wenchang Sun

Copyright © 2014 Awad A. Bakery. 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.

Linked References

  1. A. Pietsch, Operator Ideals, vol. 20 of North-Holland Mathematical Library, North-Holland Publishing, Amsterdam, The Netherlands, 1980. View at MathSciNet
  2. N. F. Mohamed and A. A. Bakery, “Mappings of type Orlicz and generalized Cesáro sequence space,” Journal of Inequalities and Applications, vol. 2013, article 186, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  3. W. Sanhan and S. Suantai, “On k-nearly uniform convex property in generalized Cesàro sequence spaces,” International Journal of Mathematics and Mathematical Sciences, no. 57, pp. 3599–3607, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. A. Bakery, “Mappings of type generalized de La Vallée Poussin's mean,” Journal of Inequalities and Applications, vol. 2013, article 518, 2013. View at Publisher · View at Google Scholar
  5. N. Şimşek, E. Savaş, and V. Karakaya, “Some geometric and topological properties of a new sequence space defined by de la Vallée-Poussin mean,” Journal of Computational Analysis and Applications, vol. 12, no. 4, pp. 768–779, 2010. View at MathSciNet
  6. N. J. Kalton, “Spaces of compact operators,” Mathematische Annalen, vol. 208, pp. 267–278, 1974. View at MathSciNet
  7. Å. Lima and E. Oja, “Ideals of finite rank operators, intersection properties of balls, and the approximation property,” Studia Mathematica, vol. 133, no. 2, pp. 175–186, 1999. View at MathSciNet
  8. G. Das and B. K. Patel, “Lacunary distribution of sequences,” Indian Journal of Pure and Applied Mathematics, vol. 20, no. 1, pp. 64–74, 1989. View at MathSciNet
  9. A. R. Freedman, J. J. Sember, and M. Raphael, “Some Cesàro-type summability spaces,” Proceedings of the London Mathematical Society, vol. 37, no. 3, pp. 508–520, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Mursaleen and T. A. Chishti, “Some spaces of lacunary sequences defined by the modulus,” Journal of Analysis, vol. 4, pp. 153–159, 1996. View at MathSciNet
  11. K. P. Lim, “Matrix transformation on certain sequence spaces,” Tamkang Journal of Mathematics, vol. 8, no. 2, pp. 213–220, 1977. View at MathSciNet
  12. K. P. Lim, “Matrix transformation in the Cesàro sequence spaces,” Kyungpook Mathematical Journal, vol. 14, pp. 221–227, 1974. View at MathSciNet
  13. T. Bilgin, “The sequence space Cess,p and related matrix transformations,” The Punjab University Journal of Mathematics, vol. 30, pp. 67–77, 1997. View at MathSciNet
  14. J.-S. Shiue, “On the Cesáro sequence spaces,” Tamkang Journal of Mathematics, vol. 1, no. 1, pp. 19–25, 1970. View at MathSciNet
  15. M. Et, Y. Altin, B. Choudhary, and B. C. Tripathy, “On some classes of sequences defined by sequences of Orlicz functions,” Mathematical Inequalities & Applications, vol. 9, no. 2, pp. 335–342, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  16. B. C. Tripathy and H. Dutta, “On some new paranormed difference sequence spaces defined by Orlicz functions,” Kyungpook Mathematical Journal, vol. 50, no. 1, pp. 59–69, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  17. B. C. Tripathy and H. Dutta, “On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary mn-statistical convergence,” Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematicaa, vol. 20, no. 1, pp. 417–430, 2012. View at MathSciNet
  18. B. C. Tripathy and S. Borgohain, “Some classes of difference sequence spaces of fuzzy real numbers defined by orlicz function,” Advances in Fuzzy Systems, vol. 2011, Article ID 216414, 6 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Rath and B. C. Tripathy, “Matrix maps on sequence spaces associated with sets of integers,” Indian Journal of Pure and Applied Mathematics, vol. 27, no. 2, pp. 197–206, 1996. View at MathSciNet
  20. B. C. Tripathy and M. Sen, “On generalized statistically convergent sequences,” Indian Journal of Pure and Applied Mathematics, vol. 32, no. 11, pp. 1689–1694, 2001. View at MathSciNet
  21. B. C. Tripathy and P. Chandra, “On some generalized difference paranormed sequence spaces associated with multiplier sequence defined by modulus function,” Analysis in Theory and Applications, vol. 27, no. 1, pp. 21–27, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  22. B. C. Tripathy, “Matrix transformation between some classes of sequences,” Journal of Mathematical Analysis and Applications, vol. 206, no. 2, pp. 448–450, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  23. B. C. Tripathy, “On generalized difference paranormed statistically convergent sequences,” Indian Journal of Pure and Applied Mathematics, vol. 35, no. 5, pp. 655–663, 2004. View at MathSciNet
  24. B. Altay and F. Başar, “Generalization of the sequence space p derived by weighted means,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 147–185, 2007. View at Publisher · View at Google Scholar