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Hyers-Ulam stability of functional equations in several variables. (English) Zbl 0836.39007
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.

MSC:
 39B62 Functional inequalities, including subadditivity, convexity, etc. 39B32 Functional equations for complex functions 39B22 Functional equations for real functions 39-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations 39-03 History of difference and functional equations
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References:
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