关于h积分的Ostrowski型不等式和Hermite-Hadamard型不等式的注记  

Notes on Ostrowski Type Inequality and Hermite-Hadamard Type Inequality for h-integrals

作　　者：时统业[1] SHI Tongye(PLA Naval Command College,Nanjing 211800,China)

机构地区：[1]海军指挥学院,江苏南京211800

出　　处：《五邑大学学报(自然科学版)》2025年第1期71-78,共8页Journal of Wuyi University(Natural Science Edition)

摘　　要：举例说明和修正了已有文献给出的h积分的Lipschitz条件下的Ostrowski型不等式和h导数有界情形下的梯形不等式.在一个特殊情况下,获得了由h积分的Hermite-Hadamard型不等式的左边部分生成的差值的估计.在h导数有界情形下,从h微积分的基本定理出发,建立了h积分的Iyengar型不等式.Ostrowski type inequality and trapezoidal inequality for h-integrals are given in existing literature.Counter examples are given illustrating these two inequalities ar e not valid,and the revised results are provided.In a special case,the estimation of the difference generated by the left part of Hermite-Hadamard type inequality for h-integrals is obtained.In the case where h-derivative is bounded,starting from the fundamental theorem of h-calculus,an Iyengar type inequality for h-integrals is established.

关 键 词：Ostrowski型不等式 Hermite-Hadamard型不等式 梯形不等式 Iyengar型不等式 h积分 h导数 

分 类 号：O178[理学—数学]