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**Solution of a stability problem of Ulam.**
*(English)*
Zbl 0878.46032

Rassias, John M. (ed.), Functional analysis, approximation theory and numerical analysis. Dedicated to Stefan Banach on his 100th birthday, Alexander Markowiç Ostrowski on his 99th birthday, Stanislaw Marcin Ulam on his 83rd birthday. Singapore: World Scientific. 241-249 (1994).

In our paper [J. Approximation Theory 57, No. 3, 268-273 (1989; Zbl 0672.41027)], we solved the following Ulam problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist” and established results involving a product of powers of norms. In this paper, we state and prove a more general version of my above theorem involving a nonnegative real-valued function.

For the entire collection see [Zbl 0867.00015].

For the entire collection see [Zbl 0867.00015].

### MSC:

46G05 | Derivatives of functions in infinite-dimensional spaces |

41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |

### Keywords:

stability problem of Ulam; isometry problem of Ulam; linear mapping near an approximately linear mapping### Citations:

Zbl 0672.41027
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\textit{J. M. Rassias}, in: Functional analysis, approximation theory and numerical analysis. Dedicated to Stefan Banach on his 100th birthday, Alexander Markowiç Ostrowski on his 99th birthday, Stanislaw Marcin Ulam on his 83rd birthday. Singapore: World Scientific. 241--249 (1994; Zbl 0878.46032)