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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An inequality suggested by Littlewood
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by Grahame Bennett PDF
Proc. Amer. Math. Soc. 100 (1987), 474-476 Request permission

Abstract:

It is shown that \[ \sum \limits _n {a_n^3} \sum \limits _{m = 1}^n {a_m^2} \sum \limits _{k = 1}^m {{a_k}} \leq \frac {3}{2}\sum \limits _n {a_n^4} {\left [ {\sum \limits _{k = 1}^n {{a_k}} } \right ]^2}\] for arbitrary nonnegative numbers ${a_1},{a_2}, \ldots$.
References
  • Grahame Bennett, Some elementary inequalities, Quart. J. Math. Oxford Ser. (2) 38 (1987), no. 152, 401–425. MR 916225, DOI 10.1093/qmath/38.4.401
    • J. Bray, Ph.D. thesis, Cambridge University.
  • J. E. Littlewood, Some new inequalities and unsolved problems, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965) Academic Press, New York, 1967, pp. 151–162. MR 0222231
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • 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