| 两个反三角平均的Schur凸性及不等式链 |
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| 引用本文： | 陈迪三.两个反三角平均的Schur凸性及不等式链[J].数学的实践与认识,2020(5):268-275. |
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| 作者姓名： | 陈迪三 |
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| 作者单位： | 桂林航天工业学院理学院;广西师范大学漓江学院理工学院 |
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| 基金项目： | 2019年度广西高校中青年教师科研基础能力提升项目(2019KY0978)。 |
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| 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.
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| 关 键 词： | 反三角平均 Schur-凸性 HERMITE-HADAMARD不等式 不等式链 |
The Schur-Convexity and Inequality Chains of Two Anti-Trigonometric Mean |
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| CHEN Di-san.The Schur-Convexity and Inequality Chains of Two Anti-Trigonometric Mean[J].Mathematics in Practice and Theory,2020(5):268-275. |
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| Authors: | CHEN Di-san |
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| Institution: | (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) |
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| Abstract: | 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. |
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| Keywords: | anti-trigonometric mean Schur-convexity Hermite-Hadamard’s inequality inequality chains |
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