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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:399

Article

Reich, L.²  Smital, J.¹  Stefankova, M.¹ 

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

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

关键词: Iterative functional equation;    Generalized Dhombres equation;    Local analytic solution;    Rational solution;    Holomorphic solution;   

DOI  :  10.1016/j.jmaa.2012.10.038

来源: Elsevier

【 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.

【 授权许可】

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