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. 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.
@article{bwmeta1.element.doi-10_1515_amsil-2016-0007,
author = {Barbara Sobek},
title = {Alienation of the Jensen, Cauchy and d'Alembert Equations},
journal = {Annales Mathematicae Silesianae},
volume = {30},
year = {2016},
pages = {181-191},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0007}
}
Barbara Sobek. Alienation of the Jensen, Cauchy and d’Alembert Equations. Annales Mathematicae Silesianae, Tome 30 (2016) pp. 181-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2016-0007/