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Time Scales Nabla Iyengar Inequalities

  • George A. AnastassiouEmail author
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 886)

Abstract

Here we present the necessary background on nabla time scales approach. Then we give general related time scales nabla Iyengar type inequalities for all basic norms. We finish with applications to specific time scales like \( \mathbb {R},\) \(\mathbb {Z}\) and \(q^{\overline{\mathbb {Z}}}\), \(q>1.\) See also [4].

References

  1. 1.
    G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)CrossRefGoogle Scholar
  2. 2.
    G. Anastassiou, Nabla time scales inequalities. Int. J. Dyn. Syst. Differ. Equ. 3(1–2), 59–83 (2011)MathSciNetzbMATHGoogle Scholar
  3. 3.
    G. Anastassiou, Time scales delta iyengar type inequalities. Int. J. Differ. Equ. (2019), http://campus.mst.edu/ijde (Accepted for publication)
  4. 4.
    G. Anastasssiou, Nabla time scales iyengar type inequalities. Adv. Dyn. Syst. Appl. (2019) (Accepted for publication)Google Scholar
  5. 5.
    D.R. Anderson, Taylor polynomials for nabla dynamic equations on times scales. Panamer. Math. J. 12(4), 17–27 (2002)MathSciNetzbMATHGoogle Scholar
  6. 6.
    D. Anderson, J. Bullock, L. Erbe, A. Peterson, H. Tran, Nabla dynamic equations on time scales. Panamer. Math. J. 13(1), 1–47 (2003)MathSciNetzbMATHGoogle Scholar
  7. 7.
    F. Atici, D. Biles, A. Lebedinsky, An application of time scales to economics. Math. Comput. Model. 43, 718–726 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Bohner, A. Peterson, Dynamic equations on time scales: an introduction with applications (Birkhaüser, Boston, 2001)CrossRefGoogle Scholar
  9. 9.
    S. Hilger, Ein Maßketten kalkül mit Annendung auf Zentrumsmannig-faltigkeiten. Ph.D. Thesis (Universität Würzburg, Germany, 1988)Google Scholar
  10. 10.
    K.S.K. Iyengar, Note on an inequality. Math. Student 6, 75–76 (1938)zbMATHGoogle Scholar
  11. 11.
    N. Martins, D. Torres, Calculus of variations on time scales with nabla derivatives. Nonlinear Anal. 71(12), 763–773 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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