关于Szász-Mirakjan算子的一个定理的证明  

On the Prove of a Theorem for Szász-Mirakjan Operators

作　　者：王小春[1] 

机构地区：[1]杭州大学数学系

出　　处：《杭州大学学报（自然科学版）》1992年第2期139-143,共5页Journal of Hangzhou University Natural Science Edition

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'.

关 键 词：连续模 S-M算子 B-算子 

分 类 号：O174[理学—数学]