Geodesic
The Schur Geometrical Convexity of the Extended Mean Values
Journal of convex analysis, Tome 15 (2008) no. 4, pp. 707-718
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We prove that the extended mean values $E(r,s;x,y)$ are Schur geometrically convex (or concave, respectively) with respect to $(x,y)\in(0,\infty)\times(0,\infty)$ if and only if $s+r\geq 0$ (or $s+r\leq 0$,respectively).
Classification : 26B25
Mots-clés : Extended mean value, Schur convex, Schur concave, Schur geometrically convex, Schur geometrically concave 
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     author = {Y. Chu and X. Zhang and G. Wang},
     title = {The {Schur} {Geometrical} {Convexity} of the {Extended} {Mean} {Values}},
     journal = {Journal of convex analysis},
     pages = {707--718},
     year = {2008},
     volume = {15},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a3/}
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Y. Chu; X. Zhang; G. Wang. The Schur Geometrical Convexity of the Extended Mean Values. Journal of convex analysis, Tome 15 (2008) no. 4, pp. 707-718. http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a3/