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Zbl 1076.39025
Chung, Jaeyoung
A distributional version of functional equations and their stabilities. (English)
[J] Nonlinear Anal., Theory Methods Appl. 62, No. 6, A, 1037-1051 (2005). ISSN 0362-546X

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].
[Jacek Chmielinski (Kraków)]

MSC 2000:: *39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains
46F10 Operations with distributions (generalized functions)

Keywords: Schwartz distributions; stability; Cauchy functional equations; Pexider functional equations; Jensen functional equations; quadratic functional equations; D'Alembert functional equations; Gelfand-Shilov generalized functions; heat kernel

Citations: Zbl 1033.39025; Zbl 1053.39043; Zbl 1076.39024

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