Abstract
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.
Highlights
Throughout the article, the n-dimensional Euclidean space is denoted by Rn, and Rn+ = {(x1, . . . , xn) | xi > 0, i = 1, . . . , n}
In 1923, Schur [1] introduced the concept of the Schur-convex function
It can be applied to many aspects, including extended mean values [2,3,4,5,6,7], isoperimetric inequalities on the polyhedron [8], theory of statistical experiments [9], gamma and digamma functions [10], combinational optimization [11], graphs and matrices [12], reliability [13], information theoretic topics [14], stochastic orderings [15], and other related fields
Summary
Throughout the article, the n-dimensional Euclidean space is denoted by Rn, and Rn+ = {(x1, . R1 is denoted by R for simplicity. In 1923, Schur [1] introduced the concept of the Schur-convex function. It can be applied to many aspects, including extended mean values [2,3,4,5,6,7], isoperimetric inequalities on the polyhedron [8], theory of statistical experiments [9], gamma and digamma functions [10], combinational optimization [11], graphs and matrices [12], reliability [13], information theoretic topics [14], stochastic orderings [15], and other related fields. The theory of majorization was enriched [18,19,20,21,22,23,24,25,26,27]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
