Recent developments of the conditional stability of the homomorphism equation. (English) Zbl 1312.39031
Summary: The issue of Ulam’s type stability of an equation is understood in the following way: When a mapping which satisfies the equation approximately (in some sense), it is “close” to a solution of it. In this expository paper, we present a survey and a discussion of selected recent results concerning such stability of the equations of homomorphisms, focussing especially on some conditional versions of them.
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B55 | Orthogonal additivity and other conditional functional equations |
Keywords:
Hyers-Ulam-Rassias stability; (orthogonal) Cauchy equation; orthogonality; restricted domain; sandwich technique; fixed point method; Hyers’ sequence; invariant mean methodReferences:
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