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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Schur-Convex Functions
and Isoperimetric Inequalities


Author: Xin-Min Zhang
Journal: Proc. Amer. Math. Soc. 126 (1998), 461-470
MSC (1991): Primary 26B25, 26D05, 26D10, 52A40, 52A41, 52B60
MathSciNet review: 1423343
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Abstract: In this paper, we establish some analytic inequalities for Schur-convex functions that are made of solutions of a second order nonlinear differential equation. We apply these analytic inequalities to obtain some geometric inequalities.


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Additional Information

Xin-Min Zhang
Affiliation: Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688
Email: zhang@mathstat.usouthal.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04151-3
PII: S 0002-9939(98)04151-3
Keywords: Doubly stochastic matrix, Schur-convex function, symmetric function, isoperimetric inequality, Bonnesen inequality, degree of irregularity
Received by editor(s): September 8, 1995
Received by editor(s) in revised form: August 11, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society