Abstract: Chen Guijing showed that for the onedimensional density functions satisfying λ-order Lipshitz conditions (λ∈（0,1） the convergence rates of kernel estimates is of o (（og n/n）^λ/2λ+1 log log n), and he conjectured that λ/2λ+1 cannot be improved （2）.In this paper we proved this conjecture being true.