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Linear functional equations in Banach modules over a \(C^*\)-algebra. (English) Zbl 1053.39044
This paper is a survey of recent results on the Ulam-Hyers-Rassias stability of linear functional equations in Banach modules over a \(C^*\)-algebra.
The reader may find the results concerning the stability of the following equations: Cauchy functional equation, Jensen functional equation, Trif functional equation, cyclic functional equation and some applications.
The methods applied are standard, mainly based on some ideas of Hyers and Rassias.
The reader may find more information in the book of the reviewer [Functional equations and inequalities in several variables (World Scientific, Singapore) (2002; Zbl 1011.39019)].

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
47B48 Linear operators on Banach algebras
46L05 General theory of \(C^*\)-algebras
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