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A distributional version of functional equations and their stabilities. (English) Zbl 1076.39025
The author considers some classical functional equations like the Cauchy, Pexider, Jensen, d’Alembert, quadratic ones in the realm of Schwartz distributions. The stability results for this equations are proved. The paper complements a collection of the author’s previous results of the similar type [e.g., J. Math. Anal. Appl. 286, No. 1, 177--186 (2003; Zbl 1033.39025); J. Math. Anal. Appl. 295, 107--114 (2004; Zbl 1053.39043); Arch. Math. 84, No. 6, 527--537 (2005; Zbl 1076.39024), reviewed above].

39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
46F10Operations with distributions (generalized functions)
Full Text: DOI
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