Generalisation of the Muirhead-Rado inequality
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- by D. E. Daykin PDF
- Proc. Amer. Math. Soc. 30 (1971), 84-86 Request permission
Abstract:
For polynomials ${f_\beta }(x)$ of n real variables $x = ({x_1},{x_2}, \cdots ,{x_n})$ of the form \[ {f_\beta }(x) = \sum \limits _i {\sum \limits _j {x_{\rho (i,1)}^{{\beta _1}{e_{j1}}}x_{\rho (i,2)}^{{\beta _2}{e_{j2}}} \cdots } } x_{\rho (i,n)}^{{\beta _n}{e_{jn}}},\] conditions are given which ensure that ${f_\alpha }(x) \leqq {f_\beta }(x)$ for all $x \geqq 0$.References
- T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Springer-Verlag, Berlin-New York, 1974 (German). Berichtigter Reprint. MR 0344997 G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, New York, 1934. R. F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinburgh Math. Soc. 21 (1903), 144-157.
- R. Rado, An inequality, J. London Math. Soc. 27 (1952), 1–6. MR 45168, DOI 10.1112/jlms/s1-27.1.1
- D. E. Daykin, Inequalities for functions of a cyclic nature, J. London Math. Soc. (2) 3 (1971), 453–462. MR 284394, DOI 10.1112/jlms/s2-3.3.453
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 84-86
- MSC: Primary 26.60
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279255-4
- MathSciNet review: 0279255