Transforming the functional equation of Gołąb-Schinzel into one of Cauchy
Abstract
It is shown that Gołąb-Schinzel's equation may be transformed into one of Cauchy's equations by an embedding and limit process concerning the general continuous solution.
References
1. J. Aczél, J. Dhombres, Functional equations in several variables, Cambridge University Press, Cambridge, 1989.
2. J. Aczél, S. Gołąb, Remarks on one-parameter subsemigroups of the affine group and their homo- and isomorphisms, Aequationes Math. 4 (1970), 1-10.
3. N. Brillouët-Belluot, On some functional equations of Gołąb-Schinzel type, Aequationes Math. 42 (1991), 239-270.
4. S. Gołąb, A. Schinzel, Sur l'équation fonctionnelle f[x + yf(x)] = f(x)f(y), Publ. Math. Debrecen 6 (1959), 113-125.
2. J. Aczél, S. Gołąb, Remarks on one-parameter subsemigroups of the affine group and their homo- and isomorphisms, Aequationes Math. 4 (1970), 1-10.
3. N. Brillouët-Belluot, On some functional equations of Gołąb-Schinzel type, Aequationes Math. 42 (1991), 239-270.
4. S. Gołąb, A. Schinzel, Sur l'équation fonctionnelle f[x + yf(x)] = f(x)f(y), Publ. Math. Debrecen 6 (1959), 113-125.
KahligP., & SchwaigerJ. (1994). Transforming the functional equation of Gołąb-Schinzel into one of Cauchy. Annales Mathematicae Silesianae, 8, 33-38. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14215
Peter Kahlig
Angewandte Analytische Meteorologie, Universität Wien, Austria Austria
Angewandte Analytische Meteorologie, Universität Wien, Austria Austria
Jens Schwaiger
Institut für Mathematik, Karl-Franzens-Universität Graz, Austria Austria
Institut für Mathematik, Karl-Franzens-Universität Graz, Austria Austria
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.
