On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (III)
Abstract
In the present paper we deal with local analytic solutions of the functional equation announced in the title. This paper is a continuation of [2] and [3].
References
1. H. Cartan, Théorie èlémentaire des fonctions analytiques d'une ounplusieurs variables complexes, Paris 1961.
2. J. Ger, On analytic solutions of the functional equation ϕ(f(x)) = g(x,ϕ(x)), [w:] Prace matematyczne 8. Prace naukowe Uniwersytetu Śląskiego nr 218, pod red. K. Szymiczka, Katowice 1978, 45-59.
3. J. Ger, On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (II), [w:] Prace matematyczne 9. Prace naukowe Uniwersytetu Śląskiego nr 275, pod red. K. Szymiczka, Katowice 1979, 74-103.
4. M. Kuczma, Analytic solutions of a linear functional equation, Ann. Polon. Math. 21 (1969), 297-303.
5. M. Kuczma, On a functional equation with divergent solutions, Ann. Polon. Math. 22 (1969), 173-178.
6. M. Kuczma, Une remarque sur les solutions analytiques d'une équation fonctionelle, Colloq. Math. 16 (1967), 93-99.
7. M. Kuczma, Functional equations in a single variable, PWN, Monografie Mat. 46, Warszawa 1968.
8. J. Matkowski, Note on a functional equation, Zeszyty Nauk. UJ. Prace Mat. 15 (1971), 109-111.
9. W. Smajdor, On the existence and uniqueness of analytic solutions of the functional equation ϕ(z) = h(z,ϕ(f(z))), Ann. Polon. Math. 19 (1967), 37-45.
2. J. Ger, On analytic solutions of the functional equation ϕ(f(x)) = g(x,ϕ(x)), [w:] Prace matematyczne 8. Prace naukowe Uniwersytetu Śląskiego nr 218, pod red. K. Szymiczka, Katowice 1978, 45-59.
3. J. Ger, On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (II), [w:] Prace matematyczne 9. Prace naukowe Uniwersytetu Śląskiego nr 275, pod red. K. Szymiczka, Katowice 1979, 74-103.
4. M. Kuczma, Analytic solutions of a linear functional equation, Ann. Polon. Math. 21 (1969), 297-303.
5. M. Kuczma, On a functional equation with divergent solutions, Ann. Polon. Math. 22 (1969), 173-178.
6. M. Kuczma, Une remarque sur les solutions analytiques d'une équation fonctionelle, Colloq. Math. 16 (1967), 93-99.
7. M. Kuczma, Functional equations in a single variable, PWN, Monografie Mat. 46, Warszawa 1968.
8. J. Matkowski, Note on a functional equation, Zeszyty Nauk. UJ. Prace Mat. 15 (1971), 109-111.
9. W. Smajdor, On the existence and uniqueness of analytic solutions of the functional equation ϕ(z) = h(z,ϕ(f(z))), Ann. Polon. Math. 19 (1967), 37-45.
GerJ. (1985). On analytic solutions of the equation ϕ(f(x)) = g(x,ϕ(x)) (III). Annales Mathematicae Silesianae, 1, 93-102. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14339
Joanna Ger
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
