In this article, the Schur-convexities of the weighted arithmetic mean of function and the extended mean values are proved. Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the extended mean values and the generalized weighted mean with two parameters and constant weight are obtained.
"NOTES ON THE SCHUR-CONVEXITY OF THE EXTENDED MEAN VALUES." Taiwanese J. Math. 9 (3) 411 - 420, 2005. https://doi.org/10.11650/twjm/1500407849