Alienation of the Jensen, Cauchy and d’Alembert Equations

Barbara Sobek. "Alienation of the Jensen, Cauchy and d’Alembert Equations." Annales Mathematicae Silesianae 30.1 (2016): 181-191. <http://eudml.org/doc/286744>.

@article{BarbaraSobek2016,
abstract = {Let (S, +) be a commutative semigroup, σ : S → S be an endomorphism with σ2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : S → K of the functional equation f(x+y)+f(x+σ(y))+g(x+y)=2f(x)+g(x)g(y)     for  x,y∈S. \[f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;\{\rm for\}\;\;x,y \in S.\] We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential Cauchy equations.},
author = {Barbara Sobek},
journal = {Annales Mathematicae Silesianae},
keywords = {Alienation; exponential Cauchy equation; Jensen equation; d’Alembert equation},
language = {eng},
number = {1},
pages = {181-191},
title = {Alienation of the Jensen, Cauchy and d’Alembert Equations},
url = {http://eudml.org/doc/286744},
volume = {30},
year = {2016},
}

TY - JOUR
AU - Barbara Sobek
TI - Alienation of the Jensen, Cauchy and d’Alembert Equations
JO - Annales Mathematicae Silesianae
PY - 2016
VL - 30
IS - 1
SP - 181
EP - 191
AB - Let (S, +) be a commutative semigroup, σ : S → S be an endomorphism with σ2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : S → K of the functional equation f(x+y)+f(x+σ(y))+g(x+y)=2f(x)+g(x)g(y)     for  x,y∈S. \[f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;{\rm for}\;\;x,y \in S.\] We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential Cauchy equations.
LA - eng
KW - Alienation; exponential Cauchy equation; Jensen equation; d’Alembert equation
UR - http://eudml.org/doc/286744
ER -