| Title:
|
Nonlinear stability of a quadratic functional equation with complex involution (English) |
| Author:
|
Saadati, Reza |
| Author:
|
Sadeghi, Ghadir |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
111-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \rightarrow Y$ satisfies
\begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray}
for all $x$, $y\in X$, then the mapping $f \colon X \rightarrow Y$ satisfies $f(x+y) + f(x-y) = 2 f(x) + 2 f(y)$ for all $x$, $y \in X$. Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method. (English) |
| Keyword:
|
quadratic mapping |
| Keyword:
|
fixed point |
| Keyword:
|
quadratic functional equation |
| Keyword:
|
generalized Hyers-Ulam stability |
| MSC:
|
39B72 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1249.39031 |
| idMR:
|
MR2813537 |
| . |
| Date available:
|
2011-06-06T14:41:10Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141560 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
