一阶导数有界条件下的梯形不等式和Ostrowski型不等式  

Trapezoid Inequalities and Ostrowski Type Inequalities for Functions with Bounded First Derivative

作　　者：时统业[1] 曾志红 Shi Tongye;Zeng Zhihong(PLA Naval Command College,Nanjing Jiangsu 211800,China;Editorial Department of Journal,Guangdong University of Education,Guangzhou Guangdong 510303,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

出　　处：《衡阳师范学院学报》2023年第3期30-36,共7页Journal of Hengyang Normal University

摘　　要：针对一阶导数有界的可微函数,利用积分恒等式和不等式∫_(a)^( b) K(t)(f′(t)-c)dt≤sup _(t∈(a,b))|f′(t)-c|∫_(a)^( b)|K(t)|dt,以及引入参数求最值的方法,建立了梯形不等式,加强了已有文献中的梯形不等式。用同样方法将结果推广到Ostrowski型不等式。Aiming at the first order differentiable functions with bounded first derivative,the trapezoid inequalities are established by using integral identities and inequality∫_(a)^( b) K(t)(f′(t)-c)dt≤sup _(t∈(a,b))|f′(t)-c|∫_(a)^( b)|K(t)|dt,and the method of introducing parameters to find the optimal value,which strengthens the trapezoid inequalities in the existing litera⁃ture.The results are extended to Ostrowski type inequalities by the same method.

关 键 词：梯形不等式 Ostrowski型不等式 一阶可微函数 

分 类 号：O178[理学—数学]