Abstract
Here we present left Caputo fractional uniform Landau-type inequalities. We give applications and we recover the original Landau inequality on R+. This chapter relies on [3].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Aglic Aljinovi\(\mathrm{\acute{c}}\), Lj. Maranguni\(\mathrm{\acute{c}}\) and J. Pe\(\mathrm{\check{c}}\)ari\(\mathrm{\acute{c}}\), On Landau type inequalities via Ostrowski inequalities, Nonlinear Functional Analysis and Applications, Vol. 10, No. 4 (2005), pp. 565–579.
G.A. Anastassiou, Fractional Differentiation Inequalities, Springer, New York, 2009.
G.A. Anastassiou, Left Caputo fractional ⋅ ∞ - Landau inequalities, Applied Math. Letters, accepted, 2011.
N. S. Barnett and S. S. Dragomir, Some Landau type inequalities for functions whose derivatives are of locally bounded variation, Tamkang Journal of Mathematics, Vol. 37, No.4, 301–308, winter 2006.
K. Diethelm, Fractional Differential Equations, On line: http://www.tu-bs.de/~diethelm/lehre/f-dgl02/fde-skript.ps.gz 2003.
Z. Ditzian, Remarks, questions and conjectures on Landau-Kolmogorov-type inequalities, Math. Inequal. Appl. 3(2000), 15–24.
G. H. Hardy and J. E. Littlewood, Some integral inequalities connected with the calculus of variations, Quarterly Journal of Mathematics, Oxford Ser. 3(1932), 241–252.
G. H. Hardy, E. Landau and J. E. Littlewood, Some inequalities satisfied by the integrals or derivatives of real or analytic functions, Mathematische Zeitschrift 39(1935), 677–695.
R. R. Kallman and G. C. Rota, On the inequality ∥f ′ ∥ 2 ≤ 4∥f∥⋅∥f”∥ in “Inequalities”, vol. II (O. Shisha, Ed), 187-192, Academic Press, New York, 1970.
E. Landau, Einige Ungleichungen f\(\mathrm{\ddot{u}}\)r zweimal differentzierban Funktionen, Proc. Lond. Math. Soc. 13 (1913), 43–49.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 George A. Anastassiou
About this chapter
Cite this chapter
Anastassiou, G.A. (2011). Left Caputo Fractional Uniform Landau Inequalities. In: Advances on Fractional Inequalities. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0703-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0703-4_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0702-7
Online ISBN: 978-1-4614-0703-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)