DISCUSSION　ON　THE　C^r－SOLUTIONS　OF　THE　ITERATED　EQUATION　λ_1f（x）＋λ_2f^2（x）＝F（x）  

作　　者：司建国 

出　　处：《Acta Mathematica Scientia》1994年第S1期53-63,共11页数学物理学报（B辑英文版）

摘　　要：In this paper, we consider the iterated equationλ1f(x) + λ2f2(x)=F(x)where f2(x)= f(f(x)), F (x) denotes known function and f(x) denotes the unknown function. There are given conditions for the existence, uniqueness and stability of C'-solutions ofthe iterated equation (*) and also there is a proved theorem for the continuous dependence of Cr-solutions of iterated equation (*) on the given function.In this paper, we consider the iterated equationλ1f(x) + λ2f2(x)=F(x)where f2(x)= f(f(x)), F (x) denotes known function and f(x) denotes the unknown function. There are given conditions for the existence, uniqueness and stability of C'-solutions ofthe iterated equation (*) and also there is a proved theorem for the continuous dependence of Cr-solutions of iterated equation (*) on the given function.

关 键 词：Iterated equation Cr-solutions Existence uniqueness Stability. 

分 类 号：O241[理学—计算数学]