宋振云

(湖北職業(yè)技術(shù)學(xué)院信息技術(shù)學(xué)院,湖北 孝感 432000)

關(guān)于P-凸函數(shù)的積分型Jensen不等式

宋振云

(湖北職業(yè)技術(shù)學(xué)院信息技術(shù)學(xué)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(jì)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(quán)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(jié)論

2 預(yù)備知識

3 定理的證明

[1]張孔生,萬建平.P-凸函數(shù)及其性質(zhì)[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2007,23(1):130-133.

[2]宋振云.P-凸函數(shù)的幾個性質(zhì)[J].湖北職業(yè)技術(shù)學(xué)院學(xué)報(bào),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(xué)科,2010,30(2):29-30.

[4]宋振云,涂瓊霞.關(guān)于P-凸函數(shù)的Hadamard型不等式[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),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(yīng)用[J].衡陽師范學(xué)院學(xué)報(bào),2011,32(3):22-23.

[6]宋振云,萬學(xué)斌.P方凸函數(shù)的性質(zhì)及Hadamard型不等式[J].阜陽師范學(xué)院學(xué)報(bào):自然科學(xué)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(xué)“十一五”規(guī)劃項(xiàng)目(2010B296).

宋振云(1958-),副教授,研究方向：高等數(shù)學(xué)教學(xué)及凸分析.

2010 MSC:15A42