宋振云

(湖北職業(yè)技術學院信息技術學院,湖北 孝感 432000)

關于P-凸函數(shù)的積分型Jensen不等式

宋振云

(湖北職業(yè)技術學院信息技術學院,湖北 孝感 432000)

基于P-凸函數(shù)的函數(shù)凸性,研究了P-凸函數(shù)的Jensen型不等式的積分形式,通過定積分的定義計算,得到了P-凸函數(shù)的積分型Jensen不等式;利用P-凸函數(shù)的一個充要條件,建立了P-凸函數(shù)的積分型Jensen不等式的加權形式.

P-凸函數(shù);離散型Jensen不等式;積分型Jensen不等式;定積分;充要條件

1 引言及結論

2 預備知識

3 定理的證明

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[2]宋振云.P-凸函數(shù)的幾個性質[J].湖北職業(yè)技術學院學報,2010,13(1):102-104.

[3]宋振云,涂瓊霞.P-凸函數(shù)的一個充要條件[J].高師理科學科,2010,30(2):29-30.

[4]宋振云,涂瓊霞.關于P-凸函數(shù)的Hadamard型不等式[J].純粹數(shù)學與應用數(shù)學,2011,27(3):313-317.

[5]宋振云.對數(shù)凸函數(shù)的積分型型Jensen不等式及其應用[J].衡陽師范學院學報,2011,32(3):22-23.

[6]宋振云,萬學斌.P方凸函數(shù)的性質及Hadamard型不等式[J].阜陽師范學院學報:自然科學版,2010,27(4):20-24.

Discussion on the integral-type Jensen inequality of P-convex function

Song Zhenyun
(School of Information and Technology,Hubei Polytechnic Institute,Xiaogan 432000,China)

Based on the function convexity of P-convex function,the integral form of Jensen-type inequality of P-convex function is studied,and the integral-type Jensen inequality of P-convex function is got by the de fi nition of de fi nite integral.In addition,the weighted form of integral-type Jensen inequality of P-convex function is established by making use of a necesssary and sufficient condition of P-convex function.

P-convex function,discrete-type Jensen inequality,integral-type Jensen inequality, de fi nite integral,necesssary and sufficient condition

O178.1

A

1008-5513(2012)01-0036-05

2011-02-10.

湖北省教育科學“十一五”規(guī)劃項目(2010B296).

宋振云(1958-),副教授,研究方向：高等數(shù)學教學及凸分析.

2010 MSC:15A42