Schur convexity and Schur-geometrically concavity of generalized exponent mean
نویسندگان
چکیده
منابع مشابه
Schur-convexity and Schur-geometrically concavity of Gini means
The monotonicity and the Schur-convexity with parameters (s, t) in R2 for fixed (x, y) and the Schur-convexity and the Schur-geometrically convexity with variables (x, y) in R++ for fixed (s, t) of Gini mean G(r, s;x, y) are discussed. Some new inequalities are obtained.
متن کاملThe Schur Convexity for the Generalized Muirhead Mean
For x,y > 0 , a,b ∈ R with a+ b = 0 , the generalized Muirhead mean is defined by M(a,b;x,y) = ( xayb+xbya 2 ) 1 a+b . In this paper, we prove that M(a,b;x,y) is Schur convex with respect to (x,y)∈ (0,∞)×(0,∞) if and only if (a,b)∈ {(a,b)∈R2 : (a−b)2 a+b > 0 & ab 0} and Schur concave with respect to (x,y) ∈ (0,∞)×(0,∞) if and only if (a,b)∈ {(a,b)∈R+ : (a−b)2 a+b & (a,b) = (0,0)}∪{(a,b) ∈ R2 : ...
متن کاملNecessary and Sufficient Conditions for the Schur Harmonic Convexity or Concavity of the Extended Mean Values
In this paper, we prove that the extended values E(r, s;x, y) are Schur harmonic convex (or concave, respectively) with respect to (x, y) ∈ (0,∞) × (0,∞) if and only if (r, s) ∈ {(r, s) : s ≥ −1, s ≥ r, s+ r + 3 ≥ 0} ∪ {(r, s) : r ≥ −1, r ≥ s, s+r+3 ≥ 0} (or {(r, s) : s ≤ −1, r ≤ −1, s+r+3 ≤ 0}, respectively).
متن کاملSchur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function
In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.
متن کامل2 00 5 Schur Positivity and Schur Log - Concavity
We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An alternative proof of this result is provided. We also give an intriguing log-concavity property of Schur functions. 1. Schur positivity conjectures The ring of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2009
ISSN: 1846-579X
DOI: 10.7153/jmi-03-22