石煥南,張靜

(1.北京聯(lián)合大學(xué)師范學(xué)院電氣信息系,北京 100011;2.北京聯(lián)合大學(xué)基礎(chǔ)部,北京 100101)

一類條件不等式的控制證明與應(yīng)用

石煥南1,張靜2

(1.北京聯(lián)合大學(xué)師范學(xué)院電氣信息系,北京 100011;2.北京聯(lián)合大學(xué)基礎(chǔ)部,北京 100101)

通過判斷相關(guān)函數(shù)的Schur凸性、Schur幾何凸性和Schur調(diào)和凸性,證明并推廣了一類條件不等式,并據(jù)此建立了某些單形不等式.

Schur凸性;Schur調(diào)和凸性;Schur幾何凸性;條件不等式;單形

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

1 定義和引理

2 主要結(jié)果及其證明

3 幾何應(yīng)用

證明由定理3的(13)式可得證.

致謝作者感謝張晗方教授給予本文的熱情幫助.

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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.

北京市屬高等學(xué)校人才強(qiáng)教計(jì)劃資助項(xiàng)目(PHR 201108407).

石煥南(1948-),教授,研究方向：解析不等式.

張靜(1975-),副教授,研究方向：解析不等式、優(yōu)化理論、數(shù)學(xué)模型.

2010 MSC:26D 15