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Zbl 0836.39007
Forti, Gian Luigi
Hyers-Ulam stability of functional equations in several variables. (English)
[J] Aequationes Math. 50, No.1-2, 143-190 (1995). ISSN 0001-9054; ISSN 1420-8903/e

This is a survey about Hyers-Ulam stability of functional equations and systems in several variables. Except for the historical background the paper contains results on the stability of Cauchy, Jensen, quadratic and polynomial equations. The author presents superstability results concerning the multiplicative Cauchy equation and some cosine and sine functional equations. Further, approximately multiplicative linear maps in Banach algebras are considered. Moreover, the stability and the superstability of other equations and systems are discussed. Some final remarks and open problems end the paper. The bibliography contains 120 items.
[A.Smajdor (Katowice)]

MSC 2000:: *39B62 Systems of functional equations
39B32 Functional equations for complex functions
39B22 Functional equations for real functions
39-00 Reference works (functional equations)
39-03 Historical (functional equations)

Keywords: historical survey; Cauchy functional equation; Jensen functional equation; quadratic functional equation; polynomial functional equation; Hyers-Ulam stability; functional equations; systems; superstability; cosine and sine functional equations; Banach algebras; bibliography

Cited in: Zbl 1219.39011 Zbl 0981.39014 Zbl 0960.39012 Zbl 0942.39013

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