Delta Time Scales Iyengar Inequalities

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


Here we give the necessary background on delta time scales approach. Then we present general related time scales delta 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 [5].


  1. 1.
    R. Agarwal, M. Bohner, Basic Calculus on time scales and some of its applications. Results Math. 35(1–2), 3–22 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: a survey. Math. Inequalities Appl. 4(4), 535–557 (2001)Google Scholar
  3. 3.
    G.A. Anastassiou, Time scales inequalities. Intern. J. Differ. Equ. 5(1), 1–23 (2010)MathSciNetGoogle Scholar
  4. 4.
    G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)CrossRefGoogle Scholar
  5. 5.
    G. Anastassiou, Time scales delta Iyengar type inequalities. Intern. J. Differ. Equ. (2019)Google Scholar
  6. 6.
    M. Bohner, G. Guisenov, The Convolution on time scales. Abstr. Appl. Anal. 2007(58373), 24 (2007)Google Scholar
  7. 7.
    M. Bohner, B. Kaymakcalan, Opial inequalities on time scales. Ann. Polon. Math. 77(1), 11–20 (2001)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Bohner, T. Matthews, Ostrowski inequalities on time scales. JIPAM J. Inequal. Pure Appl. Math. 9(1), Article 6, 8 (2008)Google Scholar
  9. 9.
    M. Bohner, A. Peterson, Dynamic equations on time scales: An Introduction with Applications (Birkhäuser, Boston, 2001)CrossRefGoogle Scholar
  10. 10.
    R. Higgins, A. Peterson, Cauchy functions and Taylor’s formula for Time scales \(T\), in Proceedings of the Sixth International Conference on Difference equations: New Progress in Difference Equations, Augsburg, Germany, 2001, eds. by B. Aulbach, S. Elaydi, G. Ladas (Chapman & Hall / CRC, Boca Raton, 2004), pp. 299–308Google Scholar
  11. 11.
    S. Hilger, Ein Maßketten-Kalkül mit Anwendung auf Zentrum-smannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, 1988Google Scholar
  12. 12.
    K.S.K. Iyengar, Note on an inequality. Math. Stud. 6, 75–76 (1938)zbMATHGoogle 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

Personalised recommendations