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A Discrete Analogue of Opial's Inequality

Published online by Cambridge University Press:  20 November 2018

James S. W. Wong
James S. W. Wong*
Affiliation:
University of Alberta, Edmonton
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In a number of papers [1] - [7], successively simpler proofs were given for the following inequality of Opial [1], in case p=1.

Theorem 1. If x(t) is absolutely continuous with x(0)=0, then for any p ≧ 0,

(1)

Equality holds only if x(t) = Kt for some constant K.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 115 - 118
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Opial, Z., Sur une inequalite. Ann. Polon. Math., 8 (1960), pages 29-32.Google Scholar
2. Olech, C., A simple proof of a certain result of Z. Opial. Ann. Polon. Math., 8 (1966), pages 61-63.Google Scholar
3. Beesack, P. R., On an integral inequality of Z. Opial. Trans. Amer. Math. Soc., 104(1966), pages 470-475.CrossRefGoogle Scholar
4. Levinson, N., On an inequality of Opial and Beesack. Proc. Amer. Math. Soc, 15(1966), pages 565-566 CrossRefGoogle Scholar
5. Mallows, C. Li., An even simpler proof of OpiaUs inequality. Proc. Amer. MathSoc, 16 (1966), page 173.Google Scholar
6. Pederson, R. N., On an inequality of Opial, Beesack and Levinson. Proc Amer. MathSoc, 15 (1966), page 174,Google Scholar
7. Hua, L. K., On an inequality of Opial. ScientiaSinica, 14 (1966), pages 789-790.Google Scholar