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Zbl 0599.39007
Skof, Fulvia
Local properties and approximation of operators. (Italian. English summary)
[J] Rend. Sem. Mat. Fis. Milano 53, 113-129 (1983). ISSN 0370-7377

This paper is connected with the theory of functional equations in the meaning of J. Aczél and more exactly with their Hyers stability [cf. {\it D. H. Hyers}, Proc. Nat. Acad. Sci. USA 27, 222-224 (1941; Zbl 0061.264)]. We state some results and problems concerning the local uniform approximation and the extension of an operator $f: D\sb f\subset {\bbfR}\to X$ (X being a Banach space) for which the condition $\Vert f(x+y)-f(x)-f(y)\Vert <\delta$ holds only in a given subset of ${\bbfR}\sp 2$ for some $\delta >0$. Similar problems are posed in relation to the condition $\Vert f(x+y)+f(x-y)-2f(x)-2f(y)\Vert <\delta$.

MSC 2000:: *39B52 Functional equations for functions with more general domains

Keywords: Hyers stability; local uniform approximation; Banach space

Citations: Zbl 0061.264

Cited in: Zbl 1170.39014 Zbl 1077.39025 Zbl 1046.39023 Zbl 1053.46029 Zbl 1050.39034 Zbl 0702.39007

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