Some properties of a class of symmetric functions |
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Authors: | Kaizhong Guan |
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Institution: | Department of Mathematics, Nanhua University, Hengyang, Hunan 421001, People's Republic of China |
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Abstract: | The Schur-convexity and Schur-geometric-convexity of a class of symmetric functions are investigated. As consequences some new proofs of the well-known Ky Fan's inequality and Shapiro's inequality are presented, respectively. We also give another proof of a problem posted by S. Gabler in S. Gabler, Aufgabe 830, Elem. Math. 3 (1980) 124-125]. Some interesting matrix and geometric inequalities are established to show the applications of our results. |
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Keywords: | Schur-convex function Schur-geometrically-convex function Ky Fan's inequality Shapiro's inequality |
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