预不变凸函数的q-Hermite-Hadamard型不等式和广义的q-Iyengar型不等式  

q-Hermite-Hadamard Type Inequalities for Preinvex Functions and Generalized q-Iyengar Type

作　　者：时统业[1] 曾志红 曹俊飞[3] SHI Tongye;ZENG Zhihong;CAO Junfei(PLA Naval Command College,Nanjing 211800,Jiangsu,China;Editorial Department of Journal,Guangdong University of Education,Guangzhou 510303,Guangdong,China;School of Mathematics,Guangdong University of Education,Guangzhou 510303,Guangdong,China)

机构地区：[1]海军指挥学院,江苏南京211800 [2]广东第二师范学院学报编辑部,广东广州510303 [3]广东第二师范学院数学学院,广东广州510303

出　　处：《汕头大学学报（自然科学版）》2024年第4期24-32,共9页Journal of Shantou University：Natural Science Edition

基　　金：广东省基础与应用基础研究基金项目(2021A1515010055);广东省重点建设学科科研能力提升项目(2021ZDJS055);广东省普通高校科研重点平台和项目-重点领域专项(2023ZDZX4042);广州市海珠区科技计划项目(海科工商信计2022-37)

摘　　要：研究量子积分的Hermite-Hadamard型不等式和Iyengar型不等式,首先建立带有一个参数的量子积分恒等式,然后用引入参数求最值的方法,建立了量子积分的广义的Iyengar型不等式;在一阶量子导数的绝对值是预不变凸函数的情形下,建立了量子积分的Hermite-Hadamard型不等式.Hermite-Hadamard type inequality and Iyengar type inequality are studied for quantum integrals.Quantum integral identities with one parameter are established.The quantum integral identities and the method of introducing parameter are used to find the optimal value.Generalized Iyengar type inequalities for quantum integrals are derived.In the case where the absolute values of the first-order quantum derivatives are preinvex function,Hermite-Hadamard type inequalities for quantum integrals are established.

关 键 词：Iyengar型不等式 Hermite-Hadamard型不等式 量子积分 预不变凸函数 

分 类 号：O178[理学—数学]