Differentiable solutions of an iterative functional equation

被引：7

作者：

Wang X. ^{[1
]}

Si J. ^{[1
]}

机构：

[1] Department of Mathematics, Binzhou Normal College, Binzhou

来源：

aequationes mathematicae | 2001年 / 61卷 / 1期

关键词：

Differentiable solution; Fixed point theorem; Iterative functional equation;

D O I：

10.1007/s000100050162

中图分类号：

学科分类号：

摘要：

Using the fixed point theorems of Schauder and Banach, in this paper we discuss the existence, uniqueness and stability of differentiable solutions of an iterative functional equation. © Birkhäuser Verlag, 2001.

引用

页码：79 / 96

页数：17

共 15 条

[1]

Kuczma M., Functional Equations in A Single Variable, (1968)

[2]

Rice R.E., Schweizer B., Sklar A., When is f(f(x)) = az2+bz + c?, Amer. Math. Monthly, 87, pp. 252-263, (1980)

[3]

Kuczma M., Choczewski B., Ger R., Iterative functional equations, Encyclopedia Math. Appl., 32, (1990)

[4]

Mukherjea A., Ratti J.S., On a functional equation involving iterates of a bijection on the unit interval, Nonlinear Anal., 7, pp. 899-908, (1983)

[5]

Dhombres J.G., Itéation linéaire d'order deux, Publ. Math. Debrecen, 24, pp. 277-287, (1977)

[6]

Zhang W., Discussion on the iterated equation ∑i=1nλifi(x) = F(x), Chinese Sci. Bull., 32, pp. 1444-1451, (1987)

[7]

Zhang W., Discussion on the differentiable solutions of the iterated equation ∑i=1nλifi(x) = F(x), Nonlinear Anal., 15, pp. 387-398, (1990)

[8]

Si J., On the monotonic continuous solutions of some iterated equation, Demonstratio Math., 29, pp. 543-547, (1996)

[9]

Si J., On analytic solutions of the equation of invariant curves, C. R. Math. Rep. Acad. Sci. Canada, 17, 1, pp. 49-52, (1995)

[10]

Si J., C2 solutions of the iterated equation ∑i=1n (x) = F(x), Acta Math. Sinica, 36, 3, pp. 348-357, (1993)

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