Stability of the Pexider functional equation

Roman Badora; Barbara Przebieracz; Peter Volkmann

Published: 2010-09-30

Vol. 24 (2010)

Stability of the Pexider functional equation

Roman Badora , Barbara Przebieracz , Peter Volkmann

Abstract

A stability result for the Pexider equation will be derived from a stability theorem published in [9] for the Cauchy functional equation. Then we discuss the quality of some constants occuring in this context; as a model case we consider functions defined on the multiplicative semigroup {1, 0}.

Keywords:

Pexider equation , stability , Tabor grupoids

Download files

PDF

Citation rules

Badora, R., Przebieracz, B., & Volkmann, P. (2010). Stability of the Pexider functional equation. Annales Mathematicae Silesianae, 24, 7–13. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14030

Similar Articles

Raghavendra G. Kulkarni, Insert a root to extract a root of quintic quickly , Annales Mathematicae Silesianae: Vol. 33 (2019)
Kazimierz Nikodem, The stability of the Pexider equation , Annales Mathematicae Silesianae: Vol. 5 (1991)
Jens Schwaiger, Connections between the completion of normed spaces over non-archimedean fields and the stability of the Cauchy equation , Annales Mathematicae Silesianae: Vol. 34 No. 1 (2020)
Beata Hejmej, Stability of functional equations in dislocated quasimetric spaces , Annales Mathematicae Silesianae: Vol. 32 (2018)
Bruce Ebanks, A Levi–Civita equation on monoids, two ways , Annales Mathematicae Silesianae: Vol. 36 No. 2 (2022)
PL. Kannappan, P.K. Sahoo, J.K. Chung, An equation associated with the distance between probability distributions , Annales Mathematicae Silesianae: Vol. 8 (1994)
Detlef Gronau, Maciej Sablik, A functional equation arising from an asymptotic formula for iterates , Annales Mathematicae Silesianae: Vol. 8 (1994)
Mohamed Akkouchi, Abdellah Bounabat, M.H. Lalaoui Rhali, Fixed point approach to the stability of an integral equation in the sense of Ulam-Hyers-Rassias , Annales Mathematicae Silesianae: Vol. 25 (2011)
Imke Toborg, Peter Volkmann, On stability of the Cauchy functional equation in groupoids , Annales Mathematicae Silesianae: Vol. 31 (2017)
Roman Ger, Justyna Sikorska, On the Cauchy equation on spheres , Annales Mathematicae Silesianae: Vol. 11 (1997)

1 2 3 4 5 6 7 8 9 10 > >>

You may also start an advanced similarity search for this article.

References

1. Gajda Z., Kominek Z., On separation theorems for subadditive and superadditive functionals, Studia Math. 100 (1991), 25–38.
2. Kominek Z., On Hyers–Ulam stability of the Pexider equation, Demonstratio Math. 37 (2004), 373–376.
3. Lifšic E.A., Ideal’no vypuklye množestva, Funkcional’. Analiz Priložen. 4 (1970), no. 4, 76–77.
4. Moszner Z., On the stability of functional equations, Aequationes Math. 77 (2009), 33–88.
5. Nikodem K., The stability of the Pexider equation, Annales Mathematicae Silesianae 5 (1991), 91–93.
6. Páles Z., Volkmann P., Luce R.D., Hyers-Ulam stability of functional equations with a square-symmetric operation, Proc. Nat. Acad. Sci. U.S.A. 95 (1998), 12772–12775.
7. Tabor Jacek, Ideally convex sets and Hyers theorem, Funkcial. Ekvac. 43 (2000), 121–125.
8. Tabor Józef, Remark 18 (at the 22nd International Symposium on Functional Equations, Oberwolfach 1984), Aequationes Math. 29 (1985), 96.
9. Volkmann P., O stabilności równań funkcyjnych o jednej zmiennej , Sem. LV, no. 11 (2001), 6 pp., Errata ibid. no. 11 bis (2003), 1 p., http://www.math.us.edu.pl/smdk. Google Scholar

Roman Badora

robadora@math.us.edu.pl

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Barbara Przebieracz

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Peter Volkmann

Affiliation:

Institut für Analysis, KIT, Germany Germany

Vol. 24 (2010)
Published: 2010-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit