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].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)
G. Anastassiou, Nabla time scales inequalities. Int. J. Dyn. Syst. Differ. Equ. 3(1–2), 59–83 (2011)
G. Anastassiou, Time scales delta iyengar type inequalities. Int. J. Differ. Equ. (2019), http://campus.mst.edu/ijde (Accepted for publication)
G. Anastasssiou, Nabla time scales iyengar type inequalities. Adv. Dyn. Syst. Appl. (2019) (Accepted for publication)
D.R. Anderson, Taylor polynomials for nabla dynamic equations on times scales. Panamer. Math. J. 12(4), 17–27 (2002)
D. Anderson, J. Bullock, L. Erbe, A. Peterson, H. Tran, Nabla dynamic equations on time scales. Panamer. Math. J. 13(1), 1–47 (2003)
F. Atici, D. Biles, A. Lebedinsky, An application of time scales to economics. Math. Comput. Model. 43, 718–726 (2006)
M. Bohner, A. Peterson, Dynamic equations on time scales: an introduction with applications (Birkhaüser, Boston, 2001)
S. Hilger, Ein Maßketten kalkül mit Annendung auf Zentrumsmannig-faltigkeiten. Ph.D. Thesis (Universität Würzburg, Germany, 1988)
K.S.K. Iyengar, Note on an inequality. Math. Student 6, 75–76 (1938)
N. Martins, D. Torres, Calculus of variations on time scales with nabla derivatives. Nonlinear Anal. 71(12), 763–773 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Anastassiou, G.A. (2020). Time Scales Nabla Iyengar Inequalities. In: Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Studies in Computational Intelligence, vol 886. Springer, Cham. https://doi.org/10.1007/978-3-030-38636-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-38636-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38635-1
Online ISBN: 978-3-030-38636-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)