Some generalization of Cauchy’s and Wilson’s functional equations on abelian groups

We find the solutions f , g , h : G → X , α : G → K of the functional equation ∑ 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 K ∈ { R , C } ....

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Bibliographic Details
Published inAequationes mathematicae Vol. 89; no. 3; pp. 591 - 603
Main Author Ukasik, Radosaw
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.06.2015
Springer Nature B.V
Subjects
Analysis
Combinatorics
Mathematical functions
Mathematics
Mathematics and Statistics
39B52
Wilson’s functional equation
Cauchy’s functional equation
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Summary:We find the solutions f , g , h : G → X , α : G → K of the functional equation ∑ 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 K ∈ { R , C } .
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-013-0244-4