Alienation of Drygas' and Cauchy's functional equations

Youssef Aissi; Driss Zeglami; Brahim Fadli

Published: 2021-04-13

Vol. 35 No. 2 (2021)

Alienation of Drygas' and Cauchy's functional equations

Youssef Aissi

, Driss Zeglami , Brahim Fadli

Abstract

Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation
f(x + y) + g(x + y) + g(x - y) = f(x)f(y) + 2g(x) + g(y) + g(-y).
We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.

Keywords:

alienation , exponential Cauchy equation , additive Cauchy equation , logarithmic Cauchy equation , Drygas' functional equation

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Aissi, Y., Zeglami, D., & Fadli, B. (2021). Alienation of Drygas’ and Cauchy’s functional equations. Annales Mathematicae Silesianae, 35(2), 131–148. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13440

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References

1. J. Aczél and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, New York, 1989.
2. M. Adam, Alienation of the quadratic and additive functional equations, Anal. Math. 45 (2019), no. 3, 449–460.
3. J. Dhombres, Relations de dépendance entre les équations fonctionnelles de Cauchy, Aequationes Math. 35 (1988), no. 2-3, 186–212.
4. W. Fechner, A characterization of quadratic-multiplicative mappings, Monatsh. Math. 164 (2011), no. 4, 383–392.
5. R. Ger, On an equation of ring homomorphisms, Publ. Math. Debrecen 52 (1998), no. 3–4, 397–417.
6. R. Ger, Ring homomorphisms equation revisited, Rocznik Nauk.-Dydakt. Prace Mat. 17 (2000), 101–115.
7. R. Ger, Additivity and exponentiality are alien to each other, Aequationes Math. 80 (2010), no. 1–2, 111–118.
8. R. Ger, Alienation of additive and logarithmic equations, Ann. Univ. Sci. Budapest. Sect. Comput. 40 (2013), 269–274.
9. R. Ger, The alienation phenomenon and associative rational operations, Ann. Math. Sil. 27 (2013), 75–88.
10. R. Ger, A short proof of alienation of additivity from quadracity, Talk at the 19th Katowice-Debrecen Winter Seminar on Functional Equations and Inequalities. Zakopane, Poland, 2019.
11. R. Ger and L. Reich, A generalized ring homomorphisms equation, Monatsh. Math. 159 (2010), no. 3, 225–233.
12. R. Ger and M. Sablik, Alien functional equations: a selective survey of results, in: J. Brzdęk et al. (eds.), Developments in Functional Equations and Related Topics, Springer Optim. Appl., 124, Springer, Cham, 2017, pp. 107–147.
13. E. Gselmann, Notes on the characterization of derivations, Acta Sci. Math. (Szeged) 78 (2012), no. 1–2, 137–145.
14. Z. Kominek and J. Sikorska, Alienation of the logarithmic and exponential functional equations, Aequationes Math. 90 (2016), no. 1, 107–121.
15. G. Maksa and M. Sablik, On the alienation of the exponential Cauchy equation and the Hosszú equation, Aequationes Math. 90 (2016), no. 1, 57–66.
16. B. Sobek, Alienation of the Jensen, Cauchy and d’Alembert equations, Ann. Math. Sil. 30 (2016), 181–191.
17. H. Stetkær, Functional Equations on Groups, World Scientific Publishing Company, Singapore, 2013.
18. K. Troczka-Pawelec and I. Tyrala, On the alienation of the Cauchy equation and the Lagrange equation, Sci. Issues Jan Długosz Univ. Częst. Math. 21 (2016), 105–111.
19. I. Tyrala, Solutions of the Dhombres-type trigonometric functional equation, Pr. Nauk. Akad. Jana Długosza Czest. Mat. 16 (2011), 87–94. Google Scholar

Youssef Aissi

yaissi94@gmail.com
https://orcid.org/0000-0003-3708-3164

Affiliation:

Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Morocco Morocco

Driss Zeglami

Affiliation:

Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Morocco Morocco

Brahim Fadli

Affiliation:

Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, Morocco Morocco

Vol. 35 No. 2 (2021)
Published: 2021-09-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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