On the alienation of the exponential Cauchy equation and the Hosszú equation
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- 作者：Gyula Maksa ; Maciej Sablik
- 关键词：Cauchy equation ; Hosszú equation ; alienation
- 刊名：Aequationes Mathematicae
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：90
- 期：1
- 页码：57-66
- 全文大小：457 KB
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Maciej Sablik (2)
1. Institute of Mathematics, University of Debrecen, Pf. 12, Debrecen, 4010, Hungary
2. Institute of Mathematics, University of Silesia in Katowice, Bankowa Street 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
In this paper, we give all the solutions \({g,h:\mathbb{R}\to\mathbb{R}}\) (the reals) of the functional equation $$g(x)g(y)-g(x+y)=h(x+y-xy)-h(x)-h(y)+h(xy) \quad(x,y\in\mathbb{R}),$$supposing additionally that h is continuous. This result is in connection with the alienation of the exponential Cauchy equation g(x + y) = g(x)g(y) and the Hosszú equation h(x + y−xy) + h(xy) = h(x) + h(y), namely it turns out that these equations are alien provided that h is continuous. Keywords Cauchy equation Hosszú equation alienation Mathematics Subject Classification Primary 39B22 Secondary 39B72 The research of the first author was supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 111651.