# On the stability of functional equations

DOI: 10.1007/s00010-008-2945-7

- Cite this article as:
- Moszner, Z. Aequ. math. (2009) 77: 33. doi:10.1007/s00010-008-2945-7

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## Summary.

We give some theorems on the stability of the equation of homomorphism, of Lobacevski’s equation, of almost Jensen’s equation, of Jensen’s equation, of Pexider’s equation, of linear equations, of Schröder’s equation, of Sincov’s equation, of modified equations of homomorphism from a group (not necessarily commutative) into a \({\mathbb{Q}}\)-topological sequentially complete vector space or into a Banach space, of the quadratic equation, of the equation of a generalized involution, of the equation of idempotency and of the translation equation. We prove that the different definitions of stability are equivalent for the majority of these equations. The boundedness stability and the stability of differential equations and the anomalies of stability are considered and open problems are formulated too.

### Mathematics Subject Classification (2000).

39B82 39B62### Keywords.

Stability*b*-stability uniformly

*b*-stability boundedness stability absolute stability of functional equations good approximate solution S-semigroup B-bounded sets equation of homomorphisms and of modified homomorphisms Lobacevski’s equation Jensen’s and modified Jensen equation Pexider’s equation linear equation Schröder’s equation Sincov’s equation quadratic equation equation of generalized involutions equation of idempotents translation equation differential equations