Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications
We investigate the conditions under which the symmetric functions Fn,k(x,r)=∏1≤i1<i2<⋯<ik≤n f(∑j=1kxijr)1/r, k=1,2,…,n, are Schur m-power convex for x∈R++n and r>0. As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which gene...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/258108 |