Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities
نویسندگان
چکیده
منابع مشابه
Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities
In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.
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 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 کاملThe Schur-convexity of the mean of a convex function
The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky’s mean is obtained and a relevant double inequality that is an extension of a known inequality is established. © 2009 Elsevier Ltd. All rights reserved.
متن کاملSome weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
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 Inequalities and Applications
سال: 2018
ISSN: 1029-242X
DOI: 10.1186/s13660-017-1605-7