Geodesic
Matrices Doubly Stochastic by Blocks
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 559-577

Voir la notice de l'article provenant de la source Cambridge University Press

The present work stems from the following classical result, due to G. H. Hardy, J. E. Littlewood, G. Pólya [7], and R. Rado [10].THEOREM 1. Concerning a pair of n-tuples x, y ε Rn, the following four statementsare equivalent:(a) for every continuous, convex function f : R → R 
Fischer, Pal; Holbrook, John A. R. Matrices Doubly Stochastic by Blocks. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 559-577. doi: 10.4153/CJM-1977-058-8
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[1] 1. Blackwell, D., Equivalent comparisons of experiments, Ann. Math. Stat. 24 (1953), 265–272. Google Scholar

[2] 2. Chong, K. M., Variation reducing properties of decreasing rearrangements, Can. J. Math. 27 (1975), 330–336. Google Scholar

[3] 3. Chong, K. M. An induction theorem for rearrangements, Can. J. Math. 28 (1976), 154–160. Google Scholar

[4] 4. Duff, G. F. D., Differences, derivatives, and decreasing rearrangements, Can. J. Math. 19 (1967), 1153–1178. Google Scholar

[5] 5. Duff, G. F. D. Integral inequalities for equimeasurable rearrangements, Can. J. Math. 22 (1970), 408–430. Google Scholar

[6] 6. Garsia, A. M., Combinatorial inequalities and smoothness of functions, Bull. Amer. Math. Soc. 82 (1976), 157–170. Google Scholar

[7] 7. Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities, 2nd edition (Cambridge U.P., 1952). Google Scholar

[8] 8. Mirsky, L., On a convex set of matrices, Archiv. der Math. 10 (1959), 88–92. Google Scholar

[9] 9. Pôlya, G., Remark on WeyVs note: Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. 36 (1950), 49–51. Google Scholar

[10] 10. Rado, R., An inequality, J. London Math. Soc. 27 (1952), 1–6. Google Scholar

[11] 11. Schur, I., Uber eine Klasse von Mittelbildungen mit Anwendungen aufdie Determinantentheorie, Sitzungsber. d. Berl. Math. Gesellsch. 22 (1923), 9–20. Google Scholar

[12] 12. Sherman, S., On a theorem of Hardy, Littlewood, Pôlya, and Blackwell, Proc. Nat. Acad. Sci. 37 (1951), 826–831. Google Scholar

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