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International Journal of Analysis
Volume 2014, Article ID 786437, 7 pages
http://dx.doi.org/10.1155/2014/786437
Research Article

On the Spectral Properties of the Weighted Mean Difference Operator over the Sequence Space

1Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar 751024, India
2Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751004, India

Received 21 December 2013; Accepted 30 April 2014; Published 16 June 2014

Academic Editor: Baruch Cahlon

Copyright © 2014 P. Baliarsingh and S. Dutta. 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. H. Polat, V. Karakaya, and N. Şimşek, “Difference sequence spaces derived by using a generalized weighted mean,” Applied Mathematics Letters, vol. 24, no. 5, pp. 608–614, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  2. B. E. Rhoades, “The fine spectra for weighted mean operators,” Pacific Journal of Mathematics, vol. 104, no. 1, pp. 219–230, 1983. View at Google Scholar · View at MathSciNet
  3. B. Altay and F. Başar, “The fine spectrum and the matrix domain of the difference operator on the sequence space lp , 0<p<1,” Communications in Mathematical Analysis, vol. 2, no. 2, pp. 1–11, 2007. View at Google Scholar · View at MathSciNet
  4. B. Altay and F. Başar, “On the fine spectrum of the difference operator on c0 and c,” Information Sciences, vol. 168, no. 1–4, pp. 217–224, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. K. Kayaduman and H. Furkan, “The fine spectra of the difference operator over the sequence spaces l1 and bv,” International Mathematical Forum, vol. 1, no. 21–24, pp. 1153–1160, 2006. View at Google Scholar · View at MathSciNet
  6. P. D. Srivastava and S. Kumar, “Fine spectrum of the generalized difference operator v on sequence space l1,” Thai Journal of Mathematics, vol. 8, no. 2, pp. 221–233, 2010. View at Google Scholar · View at MathSciNet
  7. P. D. Srivastava and S. Kumar, “On the fine spectrum of the generalized difference operator v over the sequence space c0,” Communications in Mathematical Analysis, vol. 6, no. 1, pp. 8–21, 2009. View at Google Scholar · View at MathSciNet
  8. S. Dutta and P. Baliarsingh, “On the fine spectra of the generalized rth difference operator vr on the sequence space l1,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1776–1784, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. Dutta and P. Baliarsingh, “On the spectrum of 2-nd order generalized difference operator 2 over the sequence space c0,” Boletim da Sociedade Paranaense de Matemática. 3rd Série, vol. 31, no. 2, pp. 235–244, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Dutta and P. Baliarsingh, “On a spectral classification of the operator vr over the sequence space c0,” Proceeding of National Academy of Sciences, India A, Physical Science. In press.
  11. H. Bilgiç and H. Furkan, “On the fine spectrum of the generalized difference operator Br,s over the sequence spaces lp and bvp, 1<p<,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 3, pp. 499–506, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  12. H. Bilgiç and H. Furkan, “On the fine spectrum of the operator Br,s,t over the sequence spaces l1 and bv,” Mathematical and Computer Modelling, vol. 45, no. 7-8, pp. 883–891, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Mono-graphs, Istanbul, Turkey, 2012.
  14. S. Dutta and P. Baliarsingh, “Some spectral aspects of the operator Δvr over the sequence spaces lp and bvp(1LTHEXApLTHEXA),” Chinese Journal of Mathematics, vol. 2013, Article ID 286748, 10 pages, 2013. View at Publisher · View at Google Scholar
  15. S. Dutta and P. Baliarsingh, “On the spectrum of difference operator ab over the sequence spaces lp and bvp(1LTHEXApLTHEXA),” Mathematical Sciences Letters, vol. 3, no. 2, pp. 115–120, 2014. View at Google Scholar
  16. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, New York, NY, USA, 1978. View at MathSciNet
  17. S. Goldberg, Unbounded Linear Operators, Dover, New York, NY, USA, 1985. View at MathSciNet
  18. A. Wilansky, Summability through Functional Analysis, vol. 85 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 1984. View at MathSciNet
  19. S. Dutta and P. Baliarsingh, “On some Toeplitz matrices and their inversions,” Journal of the Egyptian Mathematical Society. In press.