scholarly journals Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Huan-Nan Shi ◽  
Jing Zhang ◽  
Qing-Hua Ma
Keyword(s):  
Symmetric Function ◽  
Composite Function ◽  
Complete Symmetric Function ◽  
Schur Convexity ◽  
Harmonic Convexity

scholarly journals Schur-Convexity of a Class of Elementary Symmetric Composite Functions

2021 ◽  
Vol 66 (1) ◽  
pp. 1-19
Author(s):  
Huan-Nan Shi ◽  
◽  
Tao Zhang ◽  
Bo-Yan Xi ◽  
◽  
...  
Keyword(s):  
Convex Function ◽  
Symmetric Functions ◽  
Composite Function ◽  
Elementary Symmetric Functions ◽  
Composite Functions ◽  
Schur Convex ◽  
Harmonically Convex Function ◽  
Geometrically Convex Function ◽  
Schur Convexity ◽  
Harmonic Convexity

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 on and Schur-harmonic convexity on for a composite function of the elementary symmetric functions.

scholarly journals Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2351
Author(s):  
Tao Zhang ◽  
Alatancang Chen ◽  
Huannan Shi ◽  
B. Saheya ◽  
Boyan Xi
Keyword(s):  
Inverse Problems ◽  
Composite Function ◽  
Dual Form ◽  
Composite Functions ◽  
Special Means ◽  
Schur Convexity ◽  
Harmonic Convexity ◽  
New Inequalities

This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization.

The Schur multiplicative and harmonic convexities of the complete symmetric function

2011 ◽  
Vol 284 (5-6) ◽  
pp. 653-663 ◽  
Author(s):  
Y.-M. Chu ◽  
G.-D. Wang ◽  
X.-H. Zhang
Keyword(s):  
Symmetric Function ◽  
Complete Symmetric Function

Inequalities for Generalized Symmetric Functions

1969 ◽  
Vol 12 (5) ◽  
pp. 615-623 ◽  
Author(s):  
K.V. Menon
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
Elementary Symmetric Function ◽  
Generating Series ◽  
Image Position ◽  
Complete Symmetric Function

The generating series for the elementary symmetric function Er, the complete symmetric function Hr, are defined byrespectively.

Two inequalities for the complete symmetric functions

1978 ◽  
Vol 84 (1) ◽  
pp. 1-3 ◽  
Author(s):  
V. J. Baston
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
Positive Definite ◽  
Even Order ◽  
Image Position ◽  
Complete Symmetric Function ◽  
Special Case

In (l) Hunter proved that the complete symmetric functions of even order are positive definite by obtaining the inequalitywhere ht denotes the complete symmetric function of order t. In this note we show that the inequality can be strengthened, which, in turn, enables theorem 2 of (l) to be sharpened. We also obtain a special case of an inequality conjectured by McLeod(2).

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