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
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