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Landau's inequality

Published online by Cambridge University Press:  14 November 2011

M. K. Kwong  and
A. Zettl
M. K. Kwong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115, U.S.A.
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115, U.S.A.
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Synopsis

Landau's inequality ∥y′∥2≦4∥y∥∥y″∥ is extended to ∥y′∥2≦K(a)∥y∥1−a ∥y″ ∣y∣a∥, K(a) = 4/(l−a), 0≦ a<1. The proof is elementary and new even in the case a = 0 considered by Landau.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 161 - 163
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Hadamard, J.. Sur le module maximum d'une fonction et de ses derivées. C. R. Soc. Math. France (1914), 66–72.Google Scholar
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3Kwong, M. K. and Zettl, A.. Ramifications of Landau's inequality. Proc. Roy. Soc. Edinburgh Sect. A 86 (1981), 175–212.CrossRefGoogle Scholar
4Landau, E.. Einige Ungleichungen für zweimal diflerenzierbare Funktionen. Proc. London Math. Soc. 13 (1913), 43–49.Google Scholar