Some generalization of Cauchy's and Wilson's functional equations on abelian groups
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| 024 | 7 | 0 | |a 10.1007/s00010-013-0244-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-013-0244-4 | ||
| 100 | 1 | |a Łukasik |D Radosław |u Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland |4 aut | |
| 245 | 1 | 0 | |a Some generalization of Cauchy's and Wilson's functional equations on abelian groups |h [Elektronische Daten] |c [Radosław Łukasik] |
| 520 | 3 | |a 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 } . | |
| 540 | |a The Author(s), 2013 | ||
| 690 | 7 | |a Wilson's functional equation |2 nationallicence | |
| 690 | 7 | |a Cauchy's functional equation |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 591-603 |x 0001-9054 |q 89:3<591 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-013-0244-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-013-0244-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Łukasik |D Radosław |u Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 591-603 |x 0001-9054 |q 89:3<591 |1 2015 |2 89 |o 10 | ||