title: Schur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function.
abstract: 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.
authors.affiliation: Department of Electronic Information, Teacher's College, Beijing Union University, Beijing, 100011 People's Republic of China.
authors.forename: Huan-Nan
authors.initials: HN
authors.lastname: Shi
authors.affiliation: Basic Courses Department, Beijing Union University, Beijing, 100101 People's Republic of China.
authors.forename: Jing
authors.initials: J
authors.lastname: Zhang
authors.affiliation: College of Applied Arts and Science, Beijing Union University, Beijing, 100083 People's Republic of China.
authors.forename: Qing-Hua
authors.initials: QH
authors.lastname: Ma
keywords: Complete symmetric function; Schur-convexity; Schur-geometric convexity; Schur-harmonic convexity