两个反三角平均的Schur凸性及不等式链  

The Schur-Convexity and Inequality Chains of Two Anti-Trigonometric Mean

作　　者：陈迪三 CHEN Di-san(School of Science,Guilin University of Aerospace Technology,Guilin 541004,China;School of Science and Technology,LiJiang College of GuangXi Normal University,Guilin 541006,China)

机构地区：[1]桂林航天工业学院理学院,广西桂林541004 [2]广西师范大学漓江学院理工学院,广西桂林541006

出　　处：《数学的实践与认识》2020年第5期268-275,共8页Mathematics in Practice and Theory

基　　金：2019年度广西高校中青年教师科研基础能力提升项目(2019KY0978)。

摘　　要：关于张帆,钱伟茂所定义的四个反三角函数平均,利用Hermite-Hadamard不等式证得其中两个反三角平均:Marcsin(a,b)分别是Schur-凸,Schur-几何凸,Schur-调和凸;Marctan(a,b)分别是Schur-凹,Schur-几何凸,Schur-调和凸,并结合凸函数理论得出若干不等式链.On the four anti-trigonometric function mean defined by Zhang Fan and Qian Weimao,By using the Hadamard inequality,we obtain that two anti-trigonometric mean:(3)is Schur-convex,Schur-geometric convex,Schur-harmonic convexity,and(4) is Schur-concave,Schur-geometric convex,Schur-harmonic convexity respectively.Some Inequality chains are obtained by combining convex function theory.

关 键 词：反三角平均 Schur-凸性 HERMITE-HADAMARD不等式 不等式链 

分 类 号：O174.13[理学—数学]