Alien functional equations: a selective survey of results

R Ger, M Sablik - Developments in functional equations and related …, 2017 - Springer
We present the (relatively short) history of the “alienation” in the theory of functional
equations. The notion originally has been proposed by Dhombres (Aequationes Math 35 …

Alienation of the quadratic and additive functional equations

M Adam - Analysis Mathematica, 2019 - infona.pl
Let G, H be uniquely 2-divisible Abelian groups. We study the solutions f, g: G→ H of Pexider
type functional equation (*) $$ f (x+ y)+ f (xy)+ g (x+ y)= 2f (x)+ 2f (y)+ g (x)+ g (y), $$ f (x+ y)+ …

A generalized ring homomorphisms equation

R Ger, L Reich - Monatshefte für Mathematik, 2010 - Springer
We deal with the functional equation af (xy)+ bf (x) f (y)+ cf (x+ y)+ df (x)+ kf (y)=
0\quad\quad\quad\quad\quad\quad\quad (∗) yielding a joint generalization of equations that …

[PDF][PDF] Additivity and exponentiality are alien to each other

R Ger - Aequationes mathematicae, 2010 - researchgate.net
Let (S,+) be a (semi) group and let (R,+,.) be an integral domain. We study the solutions of a
Pexider type functional equation f (x+ y)+ g (x+ y)= f (x)+ f (y)+ g (x) g (y) for functions f and g …

[PDF][PDF] On the alienation of the exponential Cauchy equation and the Hosszú equation

G Maksa, M Sablik - Aequationes Math, 2016 - academia.edu
In this paper, we give all the solutions g, h: R→ R (the reals) of the functional equation g (x) g
(y)− g (x+ y)= h (x+ y− xy)− h (x)− h (y)+ h (xy)(x, y∈ R), supposing additionally that h is …

[PDF][PDF] Alienation of the logarithmic and exponential functional equations

Z Kominek, J Sikorska - Aequationes Math, 2016 - opus.us.edu.pl
Uniwersytet Śląski University of Silesia https://opus.us.edu.pl Publikacja / Publication
Alienation of the logarithmic and exp Page 1 Uniwersytet Śląski University of Silesia https://opus.us.edu.pl …

Notes on the characterization of derivations

E Gselmann - Acta Scientiarum Mathematicarum, 2012 - Springer
Although the characterization of ring derivations has an extensive literature, up to now, all of
the characterizations have had the following form: additivity and another property imply that …

[PDF][PDF] Alienation of Drygas' and Cauchy's functional equations

Y Aissi, D Zeglami, B Fadli - Annales Mathematicae Silesianae, 2021 - intapi.sciendo.com
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 …

Ring homomorphisms equation revisited

R Ger - 2000 - rep.up.krakow.pl
The functional equation f (x+ y)+ f (xy)= f {x)+ f (y)+ f (x) f (y)(*) has been studied by J.
Dhombres (Relations de dépendance entre les équations fonctionnelles de Cauchy …

[PDF][PDF] Alienation of additive and logarithmic equations

R Ger - Ann. Univ. Sci. Budapest. Sect. Comput, 2013 - researchgate.net
ALIENATION OF ADDITIVE AND LOGARITHMIC EQUATIONS Page 1 Annales Univ. Sci.
Budapest., Sect. Comp. 40 (2013) 269–274 ALIENATION OF ADDITIVE AND LOGARITHMIC …