On Schur Convexity of Some Symmetric Functions
<p/> <p>For <inline-formula> <graphic file="1029-242X-2010-543250-i1.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2010-543250-i2.gif"/></inline-formula>, the symmetric function <inline-formula> <gra...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/543250 |
| Summary: | <p/> <p>For <inline-formula> <graphic file="1029-242X-2010-543250-i1.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2010-543250-i2.gif"/></inline-formula>, the symmetric function <inline-formula> <graphic file="1029-242X-2010-543250-i3.gif"/></inline-formula> is defined as <inline-formula> <graphic file="1029-242X-2010-543250-i4.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2010-543250-i5.gif"/></inline-formula> are positive integers. In this paper, the Schur convexity, Schur multiplicative convexity, and Schur harmonic convexity of <inline-formula> <graphic file="1029-242X-2010-543250-i6.gif"/></inline-formula> are discussed. As consequences, several inequalities are established by use of the theory of majorization.</p> |
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| ISSN: | 1025-5834 1029-242X |