caa a22 4500 605508461 CHVBK 20210128100636.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-013-0244-4 doi (NATIONALLICENCE)springer-10.1007/s00010-013-0244-4 Łukasik Radosław Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland aut Some generalization of Cauchy's and Wilson's functional equations on abelian groups [Elektronische Daten] [Radosław Łukasik] We find the solutions $${f,g,h \colon G \to X, \alpha \colon G\to {\mathbb{K}}}$$ f , g , h : G → X , α : G → K of the functional equation $$\sum\limits_{\lambda \in K} f(x+\lambda y)=|K|g(x)+ \alpha (x)h(y),\quad x,y\in G,$$ ∑ λ ∈ K f ( x + λ y ) = | K | g ( x ) + α ( x ) h ( y ) , x , y ∈ G , where (G,+) is an abelian group, K is a finite, abelian subgroup of the automorphism group of G, X is a linear space over the field $${{\mathbb{K}} \in\{{\mathbb{R}},{\mathbb{C}} \}}$$ K ∈ { R , C } . The Author(s), 2013 Wilson's functional equation nationallicence Cauchy's functional equation nationallicence Aequationes mathematicae Springer Basel 89/3(2015-06-01), 591-603 0001-9054 89:3<591 2015 89 10 https://doi.org/10.1007/s00010-013-0244-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-013-0244-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Łukasik Radosław Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 591-603 0001-9054 89:3<591 2015 89 10