NOTES ON THE SCHUR-CONVEXITY OF THE EXTENDED MEAN VALUES

59 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A Note on Schur-Convexity of Extended Mean Values (2005, unknown): “Recently, the Schur-convexities with (x, y) of the extended mean values E(r, s; x, y) were obtained, see [13, 17].”
The Best Bounds in Gautschi-Kershaw Inequalities (2006, unknown): “The positive function g a , b ( u ) has been researched in [ 18 ] and was applied in [ 7, 10, 12, 17 ] to prove the logarithmic convexity or the Schur convexity of the extended mean values.”
Necessary and sufficient conditions such that extended mean values are Schur-convex or Schur-concave (2008, background): “The Schur-convexity of the extended mean values E(r, s; x, y) with respect to (r, s) and (x, y) are investigated in [9], [10], and [11].”
An alternative note on the Schur-convexity of the extended mean values (2006, background): “Lemma 3 ([17]).”
The Schur multiplicative and harmonic convexities of the complete symmetric function (2011, background): “Schur convexity was introduced by Schur in 1923 [46] and it has many important applications in analytic inequalities [4], [12], [22], [43], theory of statistical experiments [48], graphs and matrices [15], combinatorial optimization [25], reliability [26], gamma functions [35], information-theoretic”