An Effective Characterization of Schur-Convex Functions with Applications

References

1. F. G. Bernstein, G. Doetsch: Zur Theorie der konvexen Funktionen, Math. Ann. 76 (1915) 514–526.https://doi.org/10.1007/BF01458222Google Scholar
2. G. H. Hardy, J. E. Littlewood, G. Pólya: Some simple inequalities satisfied by convex functions, Messenger Math. 58 (1929) 145–152.Google Scholar
3. G. H. Hardy, J. E. Littlewood, G. Pólya: Inequalities, 2nd Ed., Cambridge University Press, Cambridge (1988).Google Scholar
4. L. D. Kudrjavtsev: Convex function, in: Mathematical Encyclopedia, Vol. 1, I. M. Vinogradov, V. I. Bityutskov, Yu. V. Prokhorov (eds.), Soviet Encyclopedia, Moscow (1977) 794–795 (in Russian).Google Scholar
5. A. W. Marshall, I. Olkin: Inequalities: Theory of Majorization and its Applications, Academic Press, New York (1979).Google Scholar
6. A. M. Ostrowski: Sur quelques applications des fonctions convexes an sens de I. Schur, J. Math. Pures Appl. 31 (1952) 253–282.Google Scholar
7. I. Schur: Über eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie, Sitzungsber. Berl. Math. Ges. 22 (1923) 9–20, also in: Issai Schur Collected Works, Vol. II, A. Brauer, A. Rohrbach (eds.), Springer, Berlin (1973) 418–427.Google Scholar
8. C. Stępniak: Stochastic ordering and Schur-convex functions in comparison of linear experiments, Metrika 36 (1989) 291–298.https://doi.org/10.1007/BF02614102Google Scholar
9. C. Stępniak: A note on comparison of genetic experiments, Ann. Stat. 22 (1994) 1630–1632.https://doi.org/10.1214/aos/1176325646Google Scholar