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Zbl 1076.39024
Chung, Jaeyoung
Hyers-Ulam stability theorems for Pexider equations in the space of Schwartz distributions. (English)
[J] Arch. Math. 84, No. 6, 527-537 (2005). ISSN 0003-889X; ISSN 1420-8938/e

The paper deals with stability problems for Pexider's equations (additive and exponential). The classical results are extended to spaces of generalized functions such as Schwartz's tempered distributions, Sato's Fourier hyperfunctions and Gelfand-Shilov generalized functions. Similar results for the Cauchy equation have been obtained by {\it J. Chung, S.-Y. Chung} and {\it D. Kim} [J. Math. Anal. Appl. 295, 107--114 (2004; Zbl 1053.39043)].
[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: Pexider equation; generalized functions; Hypers-Ulam stability; Schwartz's tempered distributions; Sato's Fourier hyperfunctions; Gelfand-Shilov generalized functions; Cauchy equation

Citations: Zbl 1053.39043

Cited in: Zbl 1076.39025

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