Published: 2016-09-23

Alienation of the Jensen, Cauchy and d’Alembert equations

Barbara Sobek

Abstract

Let (S,+) be a commutative semigroup, σ: SS 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: SK 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.

Domyślna okładka

Vol. 30 (2016)
Published: 2016-09-23


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.2478/amsil

Publisher
University of Silesia Press

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