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

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.