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An elementary proof of Gorny's inequality

Published online by Cambridge University Press:  14 November 2011

C. Fabry
C. Fabry
Affiliation:
Institut Mathematique, Université Catholique de Louvain, chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
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Synopsis

Gorny's inequality provides upper bounds for the sup-norms ∥f(k) of a function f over an interval [a, b] for k = 1, …, n − 1, assuming the sup-norms of f and f(n) to be given. We present a simple proof of that inequality and obtain sharper estimates of the constants contained in that inequality, compared with the original verison of Gorny.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 345 - 349
Copyright
Copyright © Royal Society of Edinburgh 1987

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