关于Ostrowski-Grüss型不等式的注记

A Note on Ostrowski-Grüss Type Inequalities

研究在导函数属于L_(2)[a,b]情况下的Ostrowski型不等式和Ostrowski-Grüss型不等式.在一阶导函数属于L_(2)[a,b]情况下,利用预Grüss不等式和引入参数求最值的方法,建立了带有一个参数的Ostrowski型不等式.通过建立与Chebychev泛函有关的不等式,得到高阶导数属于L_(2)[a,b]情况下的Ostrowski型不等式以及涉及一个函数的积分均值与其在一个子区间上的均值的差值的估计.作为特例,得到已有平均中点和梯形不等式的加强.

Ostrowski type inequality and Ostrowski-Grüss type inequality in the case of derivative function belonging to L_(2)[a,b]are studied.In the case that 1st derivative belongs to L_(2)[a,b],an Ostrowski type inequality with one parameter is established by using the pre-Grüss inequality and the method of introducing parameters to find the optimal value.By establishing the inequality associated with Chebychev functional,Ostrowski type inequality is obtained for the case where the higher-order derivatives belong to L_(2)[a,b]and the estimation for the difference between the integral mean of a function and its mean over a subinterval.As a special case,the existing mean midpoint and trapezoidal inequality are strengthened.