f(x)与Kantorovich多项式的某些关系

Some relations between f(x) and its Kantorovich polynomial

设 f为 [0 ,1 ]上的连续函数 ,Kn(f)为 f的n阶Kantorovich多项式 .证明了它们的连续模对于一切自然数n及h∈ [0 ,1 ]成立ω(Kn(f) ;h) ≤ 4ω(f;h) ,由此得到Kn(f)

Let f∈C[0,1] and K n(f) be Kantorovich polynomial of degree n of f . The moduli of continuity of f and K n(f) are denoted by ω(f;h) and ω(K n(f);h) respectively. This paper proves that ω(K n(f);h)≤4ω(f;h),h∈[0,1],n=1,2,…, thus obtains the sufficient condition for K n(f)∈Lip Mα .