Separation theorems for conditional functional equations



Abstract

We prove two separation theorems for solutions of conditional Cauchy and Jensen equations.


Keywords

sandwich theorem; separation; Hyers–Ulam stability; conditional functional equation

1. Alsina C., Garcia-Roig J.L., On a conditional Cauchy equation on rhombuses, In: Functional analysis, approximation theory and numerical analysis, 5–7, World Sci. Publishing, River Edge, NJ 1994.
2. Ger R., Sikorska J., On the Cauchy equation on spheres, Ann. Math. Sil. 11 (1997), 89–99.
3. Kaufman R., Interpolation of additive functionals, Studia Math. 27 (1966), 269–272.
4. König H., On the abstract Hahn–Banach Theorem due to Rodé, Aequationes Math. 34 (1987), 89–95.
5. Kranz P., Additive functionals on abelian semigroups, Comment. Math. Prace Mat. 16 (1972), 239–246.
6. Mazur S., Orlicz W., Sur les espaces métriques linéaires II, Studia Math. 13 (1953), 137–179.
7. Nikodem K., Páles Z., Wąsowicz S., Abstract separation theorems of Rodé type and their applications, Ann. Polon. Math. 72 (1999), 207–217.
8. Páles Z., Geometric versions of Rodé’s theorem, Rad. Mat. 8 (1992), 217–229.
9. Rodé G., Eine abstrakte Version des Satzes von Hahn–Banach, Arch. Math. (Basel) 31 (1978), 474–481.
10. Szabó Gy., A conditional Cauchy equation on normed spaces, Publ. Math. Debrecen 42 (1993), 265–271.
11. Volkmann P., Weigel H., Systeme von Funktionalgleichungen, Arch. Math. (Basel) 37 (1981), 443–449.
12. Ziółkowski M., On conditional Jensen equation, Demonstratio Math. 34 (2001), 809–818.
Download

Published : 2007-09-28


FechnerW. (2007). Separation theorems for conditional functional equations. Annales Mathematicae Silesianae, 21, 31-40. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/14060

Włodzimierz Fechner  fechner@math.us.edu.pl
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.

  1. 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.
  2. 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.
  3. 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.
  4. 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.