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A simpler proof of two inequalities of Brodlie and Everitt

Published online by Cambridge University Press:  14 November 2011

P. R. Beesack
Affiliation:
Carleton University, Ottawa, Canada

Synopsis

In 1975 K. W. Brodie and W. N. Everitt dealt with integral inequalities of the form

in the two cases T = ℝ, T = ℝ+, and obtained the best possible constants KT(μ) for all μ ε ℝ. The proof was not elementary, but an elementary proof was given in 1977 by E. T. Copson. This note shows how Copson's method can be greatly simplified so as to obtain the results in a more straightforward manner.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Brodlie, K. W. and Everitt, W. N.. On an inequality of Hardy and Littlewood. Proc. Roy. Soc. Edinburgh Sect. A 72 (1975), 179186.Google Scholar
2Copson, E. T.. On two inequalities of Brodlie and Everitt. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 329333.CrossRefGoogle Scholar
3Copson, E. T.. On two integral inequalities. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 325328.Google Scholar
4Hardy, G. H., Littlewood, J. E., and Pólya, G.. Inequalities, 2nd edn (Cambridge Univ. Press, 1952).Google Scholar