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Journal: Annales Mathematicae Silesianae

New results about quadratic functional equation on semigroups

Ahmed Akkaoui , Brahim Fadli

Language: EN | Published: 19-11-2024 | Abstract | pp. 209-222

Let S be a semigroup, let (H, +) be a uniquely 2-divisible, abelian group and let ϕ, ψ be two endomorphisms of S that need not be involutive. In this paper, we express the solutions f : S→H of the following quadratic functional equation
f(xϕ(y)) + f(ψ(y)x) = 2f(x) + 2f(y),   x,y ∈ S,
in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. Some applications of this result are presented.

2024-11-19



Journal: Annales Mathematicae Silesianae

Alienation of Drygas' and Cauchy's functional equations

Youssef Aissi , Driss Zeglami , Brahim Fadli

Language: EN | Published: 13-04-2021 | Abstract | pp. 131-148

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, which is expressed by the equation
f(x + y) + g(x + y) + g(x - y) = f(x)f(y) + 2g(x) + g(y) + g(-y).
We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.

2021-04-13



Journal: Annales Mathematicae Silesianae

Stability of functional equations and properties of groups

Gian Luigi Forti

Language: EN | Published: 09-05-2019 | Abstract | pp. 77-96

Investigating Hyers–Ulam stability of the additive Cauchy equation with domain in a group G, in order to obtain an additive function approximating the given almost additive one we need some properties of G, starting from commutativity to others more sophisticated. The aim of this survey is to present these properties and compare, as far as possible, the classes of groups
involved.

2019-05-09