Moszner, Zenon On the stability of functional equations. (English) Zbl 1207.39044 Aequationes Math. 77, No. 1-2, 33-88 (2009). 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. Cited in 1 ReviewCited in 74 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc. 39B52 Functional equations for functions with more general domains and/or ranges Keywords:stability; equation of homomorphism; Lobacevski’s equation; Jensen’s equation; Pexider’s equation; Schröder’s equation; Sincov’s equation; group; Banach space; quadratic equation; generalized involution; translation equation PDF BibTeX XML Cite \textit{Z. Moszner}, Aequationes Math. 77, No. 1--2, 33--88 (2009; Zbl 1207.39044) Full Text: DOI OpenURL