Abstract
The Schur-convex function was introduced by I. Schur in 1923, and it has many important applications in analytic inequalities, generalized means, statistics experiment, chart and matrix, combinatorial optimization, reliability, information security, random sorting, etc. So it is important that Schur-convexity for symmetric functions of several variables is researched. In this paper, Guan’s symmetric function was improved, and a class of symmetric functions were derived. By so-called Schur’s condition, Schur-convexity and Schur-geometric convexity and Schur-harmonic convexity are studied for a class of symmetric functions.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Academic Press, New York (1979)
Stepniak, C.: Stochastic Ordering and Schur-Convex Functions in Comparison of Linear Experiments. Metrika 36, 291–298 (1989)
Constantine, G.M.: Schur-Convex Functions on the Spectra of Graphs. Discrete Math. 45, 181–188 (1983)
Hwang, F.K., Rothblum, U.G.: Partition-optimization with Schur Convex Sum Objective Functions. SIAM J. Discrete Math. 18, 512–524 (2004/2005)
Hwang, F.K., Rothblum, U.G., Shepp, L.: Monotone Optimal Multipartitions using Schur Convexity with Respect to Partial Orders. SIAM J. Discrete Math. 6, 537–547 (1993)
Forcina, A., Giovagnoli, A.: Homogeneity Indices and Schur-Convex Functions. Statistica (Bologna) 42, 529–542 (1982)
Shaked, M., Shanthikumar, J.G., Tong, Y.L.: Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums. J. Multivariate Anal. 53, 293–310 (1995)
Guan, K.-Z.: Some Properties of a Class of Symmetric Functions. Journal of Mathematical Analysis and Applications 336, 70–80 (2007)
Chu, Y.M., Xia, W.F., Zhao, T.H.: Schur Convexity for a Class of Symmetric Functions. Sci. China Math. 53, 465–474 (2010)
Xia, W.-F., Chu, Y.-M.: Schur-Convexity for a Class of Symmetric Functions and Its Applications. Journal of Inequalities and Applications, Article ID 493759, 15 pages (2009)
Shi, H.-N.: Schur-Geometric Convexity for Differences of Means. Applied Mathematics E-Notes 10, 275–284 (2010)
Shi, H.-N., Jiang, Y.-M., Jiang, W.-D.: Schur-Convexity and Schur-Geometrically Concavity of Gini Mean. Comp. Math. Appl. 57, 266–274 (2009)
Xia, W.-F., Chu, Y.-M.: Schur-Convexity for a Class of Symmetric Functions and Its Applications. Journal of Inequalities and Applications, Article ID 493759, 15 pages (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Sh., Zhang, Ty., Xi, By. (2011). Schur Convexity for a Class of Symmetric Functions. In: Liu, C., Chang, J., Yang, A. (eds) Information Computing and Applications. ICICA 2011. Communications in Computer and Information Science, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27503-6_86
Download citation
DOI: https://doi.org/10.1007/978-3-642-27503-6_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27502-9
Online ISBN: 978-3-642-27503-6
eBook Packages: Computer ScienceComputer Science (R0)