Schur-harmonic convexity related to co-ordinated harmonically convex functions in plane [PDF]
Journal of Inequalities and Applications, 2019 In this paper, we investigate Schur-harmonic convexity of some functions which are obtained from the co-ordinated harmonically convex functions on a square in a plane.
N. Safaei, A. Barani
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Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function [PDF]
SpringerPlus, 2016 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.
Huan-nan Shi
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Schur convexity of the generalized geometric Bonferroni mean and the relevant inequalities [PDF]
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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The Schur Harmonic Convexity of the Hamy Symmetric Function and Its Applications
Journal of Inequalities and Applications, 2009 We prove that the Hamy symmetric function Fn(x,r)=∑1≤i1<i2<⋯<ir≤n(∏j=1rxij)1/r is Schur harmonic convex for x∈R+n.
Yuming Chu, Yupei Lv
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Schur-geometric and Schur-harmonic Convexity of an Integral Mean for Convex Functions [PDF]
Turkish Journal of Analysis and Number Theory, 2016 In the paper, Schur-geometric and Schur-harmonic convexity of an integral mean for convex functions are established.
Feng Qi, Bo-Yan Xi
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Schur-power convexity of integral mean for convex functions on the coordinates
Open Mathematics, 2023 In this article, we investigate the concepts of monotonicity, Schur-geometric convexity, Schur-harmonic convexity, and Schur-power convexity for the lower and upper limits of the integral mean, focusing on convex functions on coordinate axes. Furthermore,
Shi Huannan, Zhang Jing
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OMPLEMENTARY OF CLASSICAL MEANS WITH RESPECT TO HERON MEAN AND THEIR SCHUR CONVEXITIES [PDF]
Proceedings on Engineering Sciences, 2021 In this paper, the complementary of arithmetic mean, geometric mean, harmonic mean and contra harmonic mean with respect to Heron mean are defined. Further, by finding the partial derivatives developed the Schur convexity and Schur geometric convexity ...
K M Nagaraja +3 more
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Schur-harmonic convexity for differences of some special means in two variables [PDF]
Journal of Mathematical Inequalities, 2014 In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic, and root-square means, and establish some inequalities related to these means and differences.
Ying Wu, Feng Qi, Huan-Nan Shi
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Schur-convexity, Schur geometric and Schur harmonic convexities of dual form of a class symmetric functions [PDF]
Journal of Mathematical Inequalities, 2014 By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic con- vexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones.
Huan-Nan Shi, Jing Zhang
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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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