New Results about Quadratic Functional Equation on Semigroups
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,f\left( {x\varphi \lef...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2024-11-01
|
| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2024-0023 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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,f\left( {x\varphi \left( y \right)} \right) + f\left( {\psi \left( y \right)x} \right) = 2f\left( x \right) + 2f\left( y \right), \;\;\;\;x,y \in S,
in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. Some applications of this result are presented. |
|---|---|
| ISSN: | 2391-4238 |