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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| Format: | Article |
| Language: | English |
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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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| author | Wen Wang Shiguo Yang |
| author_facet | Wen Wang Shiguo Yang |
| author_sort | Wen Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-826f0c9e7e3747398ffd4b6791a194ed |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-826f0c9e7e3747398ffd4b6791a194ed2025-02-03T01:13:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/258108258108Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and ApplicationsWen Wang0Shiguo Yang1School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, ChinaSchool of Mathematics and Statistics, Hefei Normal University, Hefei 230601, ChinaWe 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.http://dx.doi.org/10.1155/2014/258108 |
| spellingShingle | Wen Wang Shiguo Yang Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications Abstract and Applied Analysis |
| title | Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications |
| title_full | Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications |
| title_fullStr | Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications |
| title_full_unstemmed | Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications |
| title_short | Schur m-Power Convexity of a Class of Multiplicatively Convex Functions and Applications |
| title_sort | schur m power convexity of a class of multiplicatively convex functions and applications |
| url | http://dx.doi.org/10.1155/2014/258108 |
| work_keys_str_mv | AT wenwang schurmpowerconvexityofaclassofmultiplicativelyconvexfunctionsandapplications AT shiguoyang schurmpowerconvexityofaclassofmultiplicativelyconvexfunctionsandapplications |