摘要
本文指出了《数学杂志》1984年第2期中《关于Szász-Mirakjan算子》一文中其主要定理证明的不妥之处,并给出了新的证明.
Szász-Mirakjan operators is defined by Zhou Xinlong[1] have proved the following theorem.
Theorem A Let f ∈C[0, +∞), then ||3n(f)-f||c=O(ω2(f, ))
where ω2(f,t) =sup sup |f(x)|, △h2f(x) =f(x+h) + f(x-h)-2f(x).
Let (?)(t)>0 be an increasing function, for which the following condition is satisfied
(k>1 and is fixed), then
where ||·|| is the sup-norm in [0,+∞).
In a crucial way, the proof of this theorem uses a lemma 5 in [1] But the proof of lemma 5 is in error. In stead of lemma 5 we prove Theorem A by using lemma 5'.
出处
《杭州大学学报（自然科学版）》
CSCD
1992年第2期139-143,共5页
Journal of Hangzhou University Natural Science Edition
关键词
连续模
S-M算子
B-算子
modulus of continuity
Szász-Mirakjan 算子
Bernstein算子
