Alienation of the Jensen, Cauchy and d’Alembert equations
Journal Title: Annales Mathematicae Silesianae - Year 2016, Vol 30, Issue
Abstract
Let $(S,+)$ be a commutative semigroup, $\sigma : S \to S$ be an endomorphism with $\sigma^2 = id$ 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 $f, g : S \to K$ of the functional equation $$f(x + y) + f(x + \sigma(y)) + g(x + y) = 2f(x) + g(x)g(y) \ for \ x, y \in S.$$ 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.
Authors and Affiliations
Barbara Sobek
Keywords
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- EP ID EP230429
- DOI 10.1515/amsil-2016-0007
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