부산대학교 도서관

This paper concerns a theoretical result for the compound quadrature rule $Q_nf:=\frac{1}{n}\sum^n_{i=1}\sum^s_{k=1}b_kf(\frac{1}{n}(i+1+x_k))$, where $x_k\in[0,1]$. The authors prove that the error bounds, when the ordinary modulus of continuity defined by $\omega_k(f,\delta)=\sup_{0\le x\le 1}\omega_k(f,x,\delta)$ is used, are indeed less good than those for using the $\tau$-modulus $\tau_k(f,\delta)=\int^1_0\omega_k(f,x,\delta)\,dx$.