一个偶数阶导数非负的Hermite-Hadamard型不等式及其应用  

A Hermite-Hadamard type inequality for functions of even order derivatives non-negative and its applications

作　　者：孟晴 吴艺婷 MENG Qing;WU Yiting(College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《中国计量大学学报》2022年第4期603-608,共6页Journal of China University of Metrology

基　　金：国家自然科学基金青年项目(No.11901550);浙江省自然科学基金项目(No.LY21A010016)。

摘　　要：目的:建立一个偶数阶导数非负的Hermite-Hadamard型不等式,证明一个含变限积分的函数的Schur凸性。方法:构造一个涉及高阶导数的含参数积分恒等式并利用其建立Hermite-Hadamard型不等式。作为应用,将建立的不等式用于证明一个含变限积分的函数的Schur凸性。结果:在偶数阶导数非负的条件下,得到Hermite-Hadamard不等式右侧与中间项之差的上界估计的不等式,并利用其证明一个Schur-凸函数。结论:得到一个新的Hermite-Hadamard型不等式,该不等式可用于证明函数的Schur凸性,并生成一些新的积分不等式。Aims:The purpose of this article is to provide a Hermite-Hadamard-type inequality for functions whose even order derivatives are non-negative and to verify the Schur convexity of a function containing variables limit of integral.Methods:Establishing an integral identity involving higher derivatives and utilizing it to obtain a Hermite-Hadamard-type inequality,the inequality was further used to deal with the Schur convexity of a function containing variables limit of integral.Results:Under the assumption that the even order derivatives of a function were non-negative,the upper bound estimation of differences between the right and middle terms of Hermite-Hadamard’s inequality was obtained.As applications,a new Schur-convex function was proved.Conclusions:A new inequality of Hermite-Hadamard-type is obtained,which can be used to prove the Schur convexity of a function and generate some new integral inequalities.

关 键 词：Hermite-Hadamard型不等式 凸函数 Schur-凸函数 高阶导数 

分 类 号：O178[理学—数学]