线性核Toader平均的Schur凸性和Schur几何凸性 |
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引用本文: | 李明,张小明.线性核Toader平均的Schur凸性和Schur几何凸性[J].数学的实践与认识,2014(20). |
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作者姓名: | 李明 张小明 |
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作者单位: | 中国医科大学数学教研室;浙江省海宁高级中学; |
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摘 要: | 为了研究线性核Toader平均Mr(a,b)在R_(++)2上的Schur凸性和Schur几何凸性,利用控制不等式的相关理论得到结论:当r≥1时,M_r(a,b)在R_(++)2上的Schur凸性和Schur几何凸性,利用控制不等式的相关理论得到结论:当r≥1时,M_r(a,b)在R_(++)2上是Schur凸函数;当r≤1时,Mr(a,b)在R_(++)2上是Schur凸函数;当r≤1时,Mr(a,b)在R_(++)2上是Schur凹函数;当r≥1/2时,M_r(a,b)在R_(++)2上是Schur凹函数;当r≥1/2时,M_r(a,b)在R_(++)2上是Schur几何凸函数.最后,依据M_r(a,b)的Schur凸性和Schur几何凸性建立了新的不等式.
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关 键 词: | Toader平均 Schur凸性 Schur几何凸性 拉格朗日中值定理 |
Schur-Convexity and Schur-Geometric Concavity of Toader's Mean with Linear Kernel |
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Abstract: | In order to research the Schur-convexity of Toader's mean M_r(a,b) with linear kernel on R_(++)~2,using the majorization theory we obtain that M_r(a,b) is Schur-convex function on R_(++)~2 when r≥1,is Schur-concave function on R_(++)~2 when r≤1,and is Schur-geometric convex function on R_(++)~2 when r≥(1/2).Finally,new inequalities are established on the base of the Schur-convexity and Schur-geometric concavity of M_r(a,b). |
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Keywords: | toader's mean schur-convexity schur-geometric concavity lagrange mean-value theorem |
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