On a quadratic type functional equation on locally compact abelian groups
| Autor: | Dimou Hajira, Aribou Youssef, Chahbi Abdellatif, Kabbaj Samir |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Acta Universitatis Sapientiae: Mathematica, Vol 10, Iss 1, Pp 46-55 (2018) |
| Druh dokumentu: | article |
| ISSN: | 2066-7752 2018-0004 |
| DOI: | 10.2478/ausm-2018-0004 |
| Popis: | Let (G,+) be a locally compact abelian Hausdorff group, 𝓀 is a finite automorphism group of G, κ = card𝒦 and let µ be a regular compactly supported complex-valued Borel measure on G such that μ(G)=1κ$\mu ({\rm{G}}) = {1 \over \kappa }$. We find the continuous solutions f, g : G → ℂ of the functional equation ∑k∈𝒦∑λ∈𝒦∫Gf(x+k⋅y+λ⋅s)dμ(s)=g(y)+κf(x), x,y∈G,$$\sum\limits_{k \in {\cal K}} {\sum\limits_{\lambda \in {\cal K}} {\int_{\rm{G}} {{\rm{f}}({\rm{x}} + {\rm{k}} \cdot {\rm{y}} + } \lambda \cdot {\rm{s}}){\rm{d}}\mu ({\rm{s}}) = {\rm{g}}({\rm{y}}) + \kappa {\rm{f}}({\rm{x}}),\,{\rm{x}},{\rm{y}} \in {\rm{G}},} } $$ in terms of k-additive mappings. This equations provides a common generalization of many functional equations (quadratic, Jensen’s, Cauchy equations). |
| Databáze: | Directory of Open Access Journals |
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