Ulam-Hyers-Rassias stability problem for several kinds of mappings
Let \(f\) maps a (topological) vector space into a Banach space and let \(\alpha,\beta\) be given scalars. The stability of functional equations of the form \[ f(\alpha(x+y))+f(\beta(x-y))=(\alpha+\beta)f(x)+(\alpha-\beta)f(y) \] is considered. Namely, it is shown that if the above equation is satisfied approximately only (subject to precise definitions), then \(f\) is (in some sense) close to an additive (linear) mapping. Several earlier results can be derived as corollaries.
scientific article; zbMATH DE number 6366022
scientific article