The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, so...The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.展开更多
Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric in...Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.60850005, 10771195)the Natural Science Foundation of Zhejiang Province (Grant Nos. D7080080, Y7080185,Y607128)
文摘The Schur convexity and concavity of a class of symmetric functions are discussed, and an open problem proposed by Guan in "Some properties of a class of symmetric functions" is answered. As consequences, some inequalities are established by use of the theory of majorization.
基金The Doctoral Programs Foundation(20113401110009) of Education Ministry of Chinathe Natural Science Research Project(2012kj11) of Hefei Normal Universitythe NSF(KJ2013A220) of Anhui Province
文摘Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.
