Results 21 to 30 of about 50,277 (117)

Schur-Convexity for a Class of Symmetric Functions and Its Applications

Journal of Inequalities and Applications, 2009
For x=(x1,x2,…,xn)∈R+n, the symmetric function ϕn(x,r) is defined by ϕn(x,r)=ϕn(x1,x2,…,xn;r)=∏1≤i1<i2⋯<ir≤n(∑j=1r(xij/(1+xij)))1/r, where r=1,2,…,n and i1 ...
Wei-Feng Xia, Yu-Ming Chu
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Schur-convexity for compositions of complete symmetric function dual

Journal of Inequalities and Applications, 2020
The Schur-convexity for certain compound functions involving the dual of the complete symmetric function is studied. As an application, the Schur-convexity of some special symmetric functions is discussed and some inequalities are established.
Huan-Nan Shi, Pei Wang, Jian Zhang
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Schur-Convexity of the Mean of Convex Functions for Two Variables

Axioms, 2022
The results of Schur convexity established by Elezovic and Pecaric for the average of convex functions are generalized relative to the case of the means for two-variable convex functions. As an application, some binary mean inequalities are given.
Huan-Nan Shi, Dong-Sheng Wang, Chun-Ru Fu   +2 more
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Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities

Journal of Inequalities and Applications, 2018
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 ...
Huan-Nan Shi, Shan-He Wu
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A Note on Schur-Convex Functions

Rocky Mountain Journal of Mathematics, 2000
In this note it is proved that integral rithmetic mean of convex function is Schur-convex function. Applications to Schur-convexity of logarithmic mean and gamma functions are given.
Elezović, N., Pečarić, J.
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Schur-Convexity and Schur-Geometric Convexity of Čebyšev Functional

, 2009
The Schur-convexity or concavity and the Schur-geometric convexity or concavity of the Čebyšev Functional on the upper and lower limits of the integral are discussed.
Zhang, Jian, Shi, Huan-Nan
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The Schur-convexity of the mean of a convex function

Applied Mathematics Letters, 2009
The authors establish the Schur-convexity at the upper and lower limits of the integral for the mean of a convex function. Furthermore, a new proof of the inequality \[ f\bigg(\frac{a+b}{2}\bigg)=H(0) \leq H(t) \leq H(1)= \frac1{b-a}\int^ b_ a f(x)\,dx \] obtained by \textit{S. S. Dragomir} [J. Math. Anal. Appl. 167, No. 1, 49--56 (1992; Zbl 0758.26014)
Huan-Nan Shi, Da-Mao Li, Chun Gu
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Necessary and Sufficient Conditions for Schur Geometrical Convexity of the Four-Parameter Homogeneous Means

Abstract and Applied Analysis, 2010
The necessary and sufficient conditions for Schur geometrical convexity of the four-parameter means are given. This gives a unified treatment for Schur geometrical convexity of Stolarsky and Gini means.
Zhen-Hang Yang
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Schur m-power convexity of generalized geometric Bonferroni mean involving three parameters

Journal of Inequalities and Applications, 2019
In this paper, we study the Schur m-power convexity of the generalized geometric Bonferroni mean involving three parameters. Our result provides a unified generalization to the work that was done recently by Shi and Wu concerning the Schur convexity of ...
Shan-He Wu, Yu-Ming Chu
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Schur-Convexity and Schur-Geometrically Concavity of Gini Mean

, 2007
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 R²₊₊ for fixed (s, t) of Gini mean G(r, s; x, y) are discussed.
Shi, Huan-Nan
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