Abstract
In this paper, we study the Schur multiplicative and harmonic convexities for three classes of symmetric functions de ned by Sun (2014), and a class of symmetric functions de ned by Xia and Chu (2012), and generalize the main results of Sun (2014) and Xia and Chu (2012). As applications, we establish some inequalities by use of the theory of majorization, in particular, we give some new geometric inequalities in the n-dimensional space.
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