Formal solutions of the generalized Dhombres functional equation with value one at zero

被引：1

作者：

Tomaschek, Joerg ^{[1
]}

Reich, Ludwig ^{[1
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Sci Comp, A-8010 Graz, Austria

来源：

AEQUATIONES MATHEMATICAE | 2012年 / 83卷 / 1-2期

关键词：

Complex functional equations; ANALYTIC SOLUTIONS;

D O I：

10.1007/s00010-011-0104-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study formal solutions f of the generalized Dhombres functional equation f(zf(z)) = phi(f(z)). Unlike in the situation where f(0) = w(0) and w(0) is an element of C\E where E denotes the complex roots of 1, which were already discussed, we investigate solutions f where f(0) = 1. To obtain solutions in this case we use new methods which differ from the already existing ones.

引用

页码：117 / 126

页数：10

共 8 条

[1]

Cartan H., 1966, ELEMENTARE THEORIE A, V112

[2]

Dhombres J., 1979, Some Aspects of Functional Equations

[3]

Haneczok J., 2009, GRAZER MATH BER, V353, P96

[4]

Reich L., 2005, Osterreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, V214, P3

[5] On generalized Dhombres equations with nonconstant polynomial solutions in the complex plane [J].

Reich, Ludwig ;

Smital, Jaroslav .

AEQUATIONES MATHEMATICAE, 2010, 80 (1-2) :201-208

[6] Local analytic solutions of the generalized Dhombres functional equation II [J].

Reich, Ludwig ;

Smital, Jaroslav ;

Stefankova, Marta .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) :821-829

[7] Analytic solutions of a general nonlinear functional equations near resonance [J].

Xu, B ;

Zhang, WN .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (02) :620-633

[8] Small divisor problem for an analytic q-difference equation [J].

Xu, Bing ;

Zhang, Weinian .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (01) :694-703

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