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An inequality suggested by Littlewood


Author: Grahame Bennett
Journal: Proc. Amer. Math. Soc. 100 (1987), 474-476
MSC: Primary 26D15
DOI: https://doi.org/10.1090/S0002-9939-1987-0891148-X
MathSciNet review: 891148
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Abstract: It is shown that

$\displaystyle \sum\limits_n {a_n^3} \sum\limits_{m = 1}^n {a_m^2} \sum\limits_{... ...{3}{2}\sum\limits_n {a_n^4} {\left[ {\sum\limits_{k = 1}^n {{a_k}} } \right]^2}$

for arbitrary nonnegative numbers $ {a_1},{a_2}, \ldots $.

References [Enhancements On Off] (What's this?)

  • [1] G. Bennett, Some elementary inequalities, Quart. J. Math. (to appear). MR 916225 (88k:26018)
  • [2] J. Bray, Ph.D. thesis, Cambridge University.
  • [3] J. E. Littlewood, Some new inequalities and unsolved problems, Inequalities (Ed., O. Shisha), Academic Press, New York, 1967, pp. 151-162. MR 0222231 (36:5283)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0891148-X
Article copyright: © Copyright 1987 American Mathematical Society

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