Note on polynomial functions
Abstract
In the present paper it is proved that every C-polynomial function f: X→Y is a polynomial function, provided C fulfils conditions (1), (2) and X and Y are divisible commutative groups.
References
1. J. Aczél, J.A. Baker, D.Ž. Djoković, Pl. Kannappan, F. Radó, Extensions of certain homomorphisms of subsemigroups to homomorphisms of groups, Aequationes Math. 6 (1971) 263-271.
2. R. Ger, n-Convex Functions in Linear Spaces, Aequationes Math. 10 (1974) 172-176.
3. R. Ger, M. Kuczma, On the boundedness and continuity of convex functions and additive functions, Aequationes Math. 4 (1970) 157-162.
4. R. Ger, Z. Kominek, Boundedness and continuity of additive and convex functionals, Aequationes Math. 37 (1989) 251-258.
5. Z. Kominek, Convex Functions in Linear Spaces, Prace Naukowe Uniwersytetu Śląskiego w Katowicach nr 1087, Katowice 1989, 1-70.
6. Z. Kominek, M. Kuczma, Theorem of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Archiv Math. 52 (1989) 595-602.
7. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers and Silesian University Press, Warszawa-Kraków-Katowice, 1985.
2. R. Ger, n-Convex Functions in Linear Spaces, Aequationes Math. 10 (1974) 172-176.
3. R. Ger, M. Kuczma, On the boundedness and continuity of convex functions and additive functions, Aequationes Math. 4 (1970) 157-162.
4. R. Ger, Z. Kominek, Boundedness and continuity of additive and convex functionals, Aequationes Math. 37 (1989) 251-258.
5. Z. Kominek, Convex Functions in Linear Spaces, Prace Naukowe Uniwersytetu Śląskiego w Katowicach nr 1087, Katowice 1989, 1-70.
6. Z. Kominek, M. Kuczma, Theorem of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Archiv Math. 52 (1989) 595-602.
7. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers and Silesian University Press, Warszawa-Kraków-Katowice, 1985.
KominekZ. (1993). Note on polynomial functions. Annales Mathematicae Silesianae, 7, 7-15. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14243
Zygfryd Kominek
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.
