DISCUSSION ON THE Cr-SOLUTIONS OF THE ITERATED EQUATION λ1f(x)+λ2f2(x)=F(x)

数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (S1): 53-63.

DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)

司建国

Department of Mathematics, Binzhou Teachers College, Shandong 256664, China

收稿日期:1991-11-22 出版日期:1994-12-31 发布日期:1994-12-31

DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)

Si Jianguo

Department of Mathematics, Binzhou Teachers College, Shandong 256664, China

Received:1991-11-22 Online:1994-12-31 Published:1994-12-31

摘要/Abstract

摘要： In this paper, we consider the iterated equation
λ₁f(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^r-solutions of the iterated equation (*) and also there is a proved theorem for the continuous dependence of C^r-solutions of iterated equation (*) on the given function.

关键词: Iterated equation, C^r-solutions, Existence, uniqueness, Stability

Abstract: In this paper, we consider the iterated equation
λ₁f(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^r-solutions of the iterated equation (*) and also there is a proved theorem for the continuous dependence of C^r-solutions of iterated equation (*) on the given function.

Key words: Iterated equation, C^r-solutions, Existence, uniqueness, Stability

司建国. DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)[J]. 数学物理学报(英文版), 1994, 14(S1): 53-63.

Si Jianguo. DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)[J]. Acta mathematica scientia,Series B, 1994, 14(S1): 53-63.

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DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)

DISCUSSION ON THE C^r-SOLUTIONS OF THE ITERATED EQUATION λ₁f(x)+λ₂f²(x)=F(x)

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