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On two integral inequalities*
Published online by Cambridge University Press: 14 February 2012
Synopsis
In 1932, Hardy and Littlewood [1] proved the inequality
The constant 4 is best possible; equality occurs when f(x) = A Y(Bx), where
y(x) = e−½x sin (x sin y−y) (y = ⅓π), (x ≧ o)
and A and B (>0) are constants. In [2], three proofs are given. The inequality has also been discussed in [3, 4]. A very elementary proof in which the function Y(x) emerges naturally is given in this paper.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 325 - 328
- Copyright
- Copyright © Royal Society of Edinburgh 1977
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