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.
作者
时统业
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)
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