设:f(x)∈AC[o,A),并f(0)=f(h)=0.则有integral from n=0 to h(|f(x)f(x)|dx)≤h/4 integral from n=0 to h(|f'(x)|~2dx)这个不等式叫做Opial不等式.许多数学家对它曾进行过研究.在此我们给予有意义的改进:integral from n=0 to h (|...
假设y(x)在[0,a]上绝对连续,且y(0)=0,则integral from n=0 to a(|y(x)·y′(x)|dx)≤a/2 integral from n=0 to a(|y′(x)|~2dx) (1)当且仅当y′(x)=b(常数)时,等号成立 (1)式叫Opial不等式 华罗庚把(1)式进行了推广。