Inequalities of karamata, schur and muirhead, and some applications

Teaching of Mathematics

Volumn 8, Issue 1, 2005, Pages 31-45

  Kadelburg, Zoran ^a   Dukić, Dušan ^b   Lukić, Milivoje ^a   Matić, Ivan ^c  

^a Faculty of Mathematics   (Serbia)

^b UNIVERSITY OF TORONTO   (Canada)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Divided difference; Karamata s inequality; Muirhead s inequality; Petrovi s inequality; Relation of majorization; Schur s inequality; Steffensen s inequality

Indexed keywords

EID: 77952556419     PISSN: 14514966     EISSN: 24061077     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. D. Dukić, V. Janković, I. Matić, N. Petrović, The IMO Compendium, Springer, 2006.
2. L. Fuchs, AnewproofofaninequalityofHardy-Littlewood-Pólya, Math. Tidsskr. B. (1947), 53–54.
3. G. H. Hardy, J. E. Littlewood, G. Pólya, Some simple inequalities satisfied by convex function, Messenger Math. 58 (1928/29), 145–152.
4. G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, 2nd ed., Cambridge 1952.
5. A. I. Hrabrov, Around Mongolian inequality (in Russian), Matematicheskoe prosveshchenie, 3, 7 (2003), 149–162.
6. J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30 (1906), 175–193.
7. Z. Kadelburg, D. Dukić, M. Lukić, I. Matić, Inequalities (in Serbian), Društvo matematičara Srbije, Beograd, 2003.
8. J. Karamata, Sur une inégalité relative aux fonctions convexes, Publ. Math. Univ. Belgrade 1 (1932), 145–148.
9. M. Marjanović, Some inequalities with convex functions, Publ. de l’Inst. Math. (Belgrade) 8 (22) (1968), 66–68.
10. M. Marjanović, Convex and concave functions and corresponding inequalities (in Serbian), Nastava Matematike XL, 1–2 (1994), pp. 1–11 and 3–4 (1995), pp. 1–14, Društvo matematičara Srbije, Beograd.
11. D. S. Mitrinović (in cooperation with P. M. Vasić), Analytic Inequalities, Springer, 1970.
12. 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.
13. D. Nomirovskiĭ, Karamata’s Inequality (in Russian), Kvant, 4 (2003), 43–45.
14. M. Petrovitch, Sur une fonctionelle, Publ. Math. Univ. Belgrade 1 (1932), 149–156.
15. I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen die Determinanten, Theorie Sitzungsler, Berlin, Math. Gesellschaft 22 (1923), 9–20.
16. J. E. Steffensen, On a generalization of certain inequalities by Tchebychef and Jensen, Skand. Aktuarietidskr. (1925), 137–147.
17. J. E. Steffensen, Bounds of certain trigonometric integrals, Tenth Scand. Math. Congress 1946, 181–186, Copenhagen, Gjellerups, 1947.
18. G. Szegö, Über eine Verallgemeinerung des Dirichletschen Integrals, Math. Zeitschrift, 52 (1950), 676–685.
19. M. Tomić, Gauss’ theorem on the centroid and its applications (in Serbian), Mat. Vesnik 1, 1 (1949), 31–40.
20. H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A., 35 (1949), 408–411.