On generalized Dhombres equations with non-constant rational solutions in the complex plane

被引：2

作者：

Reich, L. ^{[2
]}

Smital, J. ^{[1
]}

Stefankova, M. ^{[1
]}

机构：

[1] Silesian Univ, Math Inst, CZ-74601 Opava, Czech Republic

[2] Karl Franzens Univ Graz, Inst Math, A-8010 Graz, Austria

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 399卷 / 02期

关键词：

Iterative functional equation; Generalized Dhombres equation; Local analytic solution; Rational solution; Holomorphic solution; FUNCTIONAL-EQUATION;

D O I：

10.1016/j.jmaa.2012.10.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the generalized Dhombres functional equations f (zf (z)) = phi(f (z)) which have a non-constant rational solution f(0), holomorphic at 0, with f(0)(0) = w(0), under the assumption that phi is a non-constant meromorphic function, holomorphic at w(0). All rational solutions of such an equation which are holomorphic at 0 and all formal solutions are determined. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：542 / 550

页数：9

共 9 条

[1]

Dhombres J., 1975, C R ACAD SCI PARIS A, V28, P809

[2]

Kuczma M., 1994, ENCY MATH ITS APPL, V32

[3] The holomorphic solutions of the generalized Dhombres functional equation [J].

Reich, L. ;

Smital, J. ;

Stefankova, M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 333 (02) :880-888

[4] Functional equation of Dhombres type - a simple equation with many open problems [J].

Reich, L. ;

Smital, J. .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2009, 15 (11-12) :1179-1191

[5]

Reich L., 2006, OSTERREICH AKAD W MN, V241, P3

[6]

Reich L., 1994, AARHUS U VARIOUS PUB, V42, P245

[7] 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

[8]

Tomaschek J., 2011, 358 KARL FRANZ U GRA

[9] Formal solutions of the generalized Dhombres functional equation with value one at zero [J].

Tomaschek, Joerg ;

Reich, Ludwig .

AEQUATIONES MATHEMATICAE, 2012, 83 (1-2) :117-126

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