Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for Lehmer mean of n variables are investigated, and some mean value inequalities of n variables are established.

Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value inequalities of two variables are established.

The Schur-m power convexity of a mean for two variables with three parameters is investigated and a judging condition about the Schur-m power convexity of a mean for two variables with three parameters is given.

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In this paper, we discuss the Schur convexity, the Schur geometric convexity and Schur harmonic convexity of the mixed mean of n variables involving three parameters. As an application, we have established some inequalities of the Ky Fan type related to the mixed mean of n variables, and the lower bound inequality of Gini mean for n variables is given.