Nice results about quadratic type functional equations on semigroups
| Autor: | Driss Zeglami, B. Fadli, A. Akkaoui, M. El Fatini |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Semigroup
Applied Mathematics General Mathematics Linear space 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Combinatorics Quadratic equation Functional equation Discrete Mathematics and Combinatorics 0101 mathematics Abelian group Linear combination Mathematics |
| Zdroj: | Aequationes mathematicae. 94:83-96 |
| ISSN: | 1420-8903 0001-9054 |
| DOI: | 10.1007/s00010-019-00653-w |
| Popis: | Let $$(S,+)$$ be an abelian semigroup, let $$\sigma $$ be an involution of S, let X be a linear space over the field $${\mathbb {K}}\in \{{\mathbb {R}},{\mathbb {C}}\}$$ and let $$\mu $$,$$\nu $$ be linear combinations of Dirac measures. In the present paper, we find the general solution $$f:S\rightarrow X$$ of the following functional equation $$\begin{aligned} \int _{S}f(x+y+t)d\mu (t)+\int _{S}f(x+\sigma (y)+t)d\nu (t)=f(x)+f(y), \ \ \ x,y \in S, \end{aligned}$$in terms of additive and bi-additive maps. Many consequences of this result are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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