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

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• 作者：Rados?aw ?ukasik
• 关键词：39B52 ; Wilson’s functional equation ; Cauchy’s functional equation
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：591-603
• 全文大小：476 KB
• 参考文献：1.Acél J., Chung J.K., Ng C.T.: Symmetric Second Differences in Product form on Groups. Topics in Mathematical Analysis, 1-2, Series in Pure Mathematics, vol. 11. World Scientific Publishing, Teaneck (1989)
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  6.?ukasik, R.: Some generalization of the quadratic and Wilson’s functional equation. Aequ. Math. doi:10.-007/?s00010-013-0185-y
  7.Stetk?r H.: On a signed cosine equation of N summands. Aequ. Math. 51(3), 294-02 (1996)View Article MATH
  8.Stetk?r H.: Wilson’s functional equation on \({{\mathbb{C}}}\) . Aequ. Math. 53(1-2), 91-07 (1997)View Article MATH
  9.Stetk?r H.: Functional equation on abelian groups with involution. Aequ. Math. 54(1-), 144-72 (1997)View Article MATH
  10.Stetk?r H.: Functional equations involving means of functions on the complex plane. Aequ. Math. 56, 47-2 (1998)View Article MATH
  
• 作者单位：Rados?aw ?ukasik (1)
  
  1. Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

We find the solutions \({f,g,h \colon G \to X, \alpha \colon G\to {\mathbb{K}}}\) of the functional equation $$\sum\limits_{\lambda \in K} f(x+\lambda y)=|K|g(x)+ \alpha (x)h(y),\quad x,y\in G,$$