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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/258108 |
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| Summary: | 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
generalizes some known results. By applying the theory of
majorization, several inequalities involving the pth power mean and
the arithmetic, the geometric, or the harmonic means are presented. |
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| ISSN: | 1085-3375 1687-0409 |