THE TEACHING OF MATHEMATICS

THE TEACHING OF MATHEMATICS
Inequalities of Karamata, Schur and Muirhead, and some applications
Zoran Kadelburg, Dušan Djukić, Milivoje Lukić and Ivan Matić

Abstract

Three classical general inequalities---those of Karamata, Schur and Muirhead---are proved in this article. They can be used in proving other inequalities, particularly those appearing as problems in mathematical competitions, including International Mathematical Olympiads. Some problems of this kind are given as examples. Several related inequalities---those of Petrović, Steffensen and Szegö---are treated, as well.

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Keywords: Relation of majorization, divided difference, Karamata's inequality, Petrović's inequality, Steffensen's inequality, Schur's inequality, Muirhead's inequality.

Pages:  31$-$45     

Volume  VIII ,  Issue  1 ,  2005