. "333" . "19610" . . . "The holomorphic solutions of the generalized Dhombres functional equation" . "Holomorfn\u00ED \u0159e\u0161en\u00ED zobecn\u011Bn\u00E9 Dhombresovy funkcion\u00E1ln\u00ED rovnice"@cs . "P(GA201/06/0318), Z(MSM4781305904)" . "NL - Nizozemsko" . "3"^^ . "The holomorphic solutions of the generalized Dhombres functional equation"@en . . "Sm\u00EDtal, Jaroslav" . . "880;888" . . . . . "[7B653C5B8D49]" . "0022-247X" . "9"^^ . . "424699" . "We study holomorphic solutions f of the generalized Dhombres equation f(zf(z))=g(f(z)), for z in C, where g is in the class E of entire functions. We show, among others, that there is a nowhere dense subset E' of E such that for every g in E - E', any solution f vanishes at 0 and hence, satisfies the conditions for local analytic solutions with fixed point 0 from our recent paper. Consequently, we are able to provide a characterization of solutions in the typical case where g is in E-E'. We also show that for polynomial g any holomorphic solution on the punctured C can be extended to the whole of C. Using this, in special cases, we can provide a characterization of the analytic solutions in C."@en . "entire function; locally analytic function; iterative functional equation; typical solution"@en . "The holomorphic solutions of the generalized Dhombres functional equation"@en . "\u0160tef\u00E1nkov\u00E1, Marta" . "The holomorphic solutions of the generalized Dhombres functional equation" . "We study holomorphic solutions f of the generalized Dhombres equation f(zf(z))=g(f(z)), for z in C, where g is in the class E of entire functions. We show, among others, that there is a nowhere dense subset E' of E such that for every g in E - E', any solution f vanishes at 0 and hence, satisfies the conditions for local analytic solutions with fixed point 0 from our recent paper. Consequently, we are able to provide a characterization of solutions in the typical case where g is in E-E'. We also show that for polynomial g any holomorphic solution on the punctured C can be extended to the whole of C. Using this, in special cases, we can provide a characterization of the analytic solutions in C." . . "Journal of Mathematical Analysis and Applications" . . . "Holomorfn\u00ED \u0159e\u0161en\u00ED zobecn\u011Bn\u00E9 Dhombresovy funkcion\u00E1ln\u00ED rovnice"@cs . . "Studujeme holomorfn\u00ED \u0159e\u0161en\u00ED f zobecn\u011Bn\u00E9 Dhombresovy funkcion\u00E1ln\u00ED rovnice f(zf(z))=g(f(z)), pro komplexni z, kde g pat\u0159\u00ED do t\u0159\u00EDdy E v\u0161ech cel\u00FDch funkc\u00ED. Dokazujeme, \u017Ee krom\u011B jin\u00E9ho existuje \u0159\u00EDdk\u00E1 podmno\u017Eina E' mno\u017Einy E tak, \u017Ee pro ka\u017Ed\u00E9 g z E-E', ka\u017Ed\u00E9 \u0159e\u0161en\u00ED f m\u00E1 v bod\u011B 0 hodnotu 0 a tedy spl\u0148uje podm\u00EDnky pro lok\u00E1lnn\u011B analytick\u00E1 \u0159e\u0161en\u00ED s pevn\u00FDm bodem 0 z na\u0161eho p\u0159edch\u00E1zej\u00EDc\u00EDho \u010Dl\u00E1nku. D\u016Fsledkem je to, \u017Ee lze naj\u00EDt charakterizaci \u0159e\u0161en\u00ED v typick\u00E9m p\u0159\u00EDpad\u011B kdy g pat\u0159\u00ED do E-E'. Ukazujeme t\u00E9\u017E, \u017Ee pro polynomick\u00E1 g ka\u017Ed\u00E9 holomorfn\u00ED \u0159e\u0161en\u00ED na C bez nuly lze roz\u0161\u00ED\u0159it na celou mno\u017Einu C. Pomoc\u00ED toho ve speci\u00E1ln\u00EDch p\u0159\u00EDpadech lze charakterizovat analytick\u00E1 \u0159e\u0161en\u00ED v C."@cs . . "RIV/47813059:19610/07:#0000199!RIV08-MSM-19610___" . . "RIV/47813059:19610/07:#0000199" . . "2" . "Reich, Ludwig" . . "2"^^ . .