一类条件不等式的控制证明与应用

石焕南,张静

(1.北京联合大学师范学院电气信息系,北京 100011;2.北京联合大学基础部,北京 100101)

一类条件不等式的控制证明与应用

石焕南1,张静2

(1.北京联合大学师范学院电气信息系,北京 100011;2.北京联合大学基础部,北京 100101)

通过判断相关函数的Schur凸性、Schur几何凸性和Schur调和凸性,证明并推广了一类条件不等式,并据此建立了某些单形不等式.

Schur凸性;Schur调和凸性;Schur几何凸性;条件不等式;单形

DO I：10.3969/j.issn.1008-5513.2013.05.001

1 定义和引理

2 主要结果及其证明

3 几何应用

证明由定理3的(13)式可得证.

致谢作者感谢张晗方教授给予本文的热情帮助.

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M a jorized p roof and app lications for a class of cond itional inequality

Shi Huannan1,Zhang Jing2

(1.Departm ent of E lectronic Inform ation,Teacher′s College of Beijing Union University,
Beijing 100011,China;
2.Basic Courses Department,Beijing Union University,Beijing 100101,China)

To determ ine Schur convexity,Schur-geometric and harmonic convexities of the related function,a class of conditional inequality is p roved.As an application,several sim plex inequalities are obtained.

Schu r-convexity,Schu r harm onic convexity,Schu r geom etric convexity,cond itional inequality, sim p lex

O178

A

1008-5513(2013)05-0441-09

2013-05-22.

北京市属高等学校人才强教计划资助项目(PHR 201108407).

石焕南(1948-),教授,研究方向：解析不等式.

张静(1975-),副教授,研究方向：解析不等式、优化理论、数学模型.

2010 MSC:26D 15