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Two series inequalities*

Published online by Cambridge University Press:  14 November 2011

E. T. Copson
E. T. Copson
Affiliation:
University of St Andrews
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Synopsis

In 1932, Hardy and Littlewood proved the inequalities

The best possible values of the constants K1 and K2 being 1 and 4 respectively. The object of this paper is to prove analogous results for infinite series in which the derivative of the real function f is replaced by the finite difference

of a sequence {an} of real numbers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 109 - 114
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Hardy, G. H. and Littlewood, J. E.. On certain inequalities connected with the calculus of variations. J. London Math. Soc. 5 (1930), 283–290.Google Scholar
2Hardy, G. H., Littlewood, J. E. and Pólya, G.. Inequalities (Cambridge Univ. Press, 1931).Google Scholar