Superstability of the Cauchy, Jensen and isometry equations
The author generalizes the results of \textit{J. Tabor} [Result Math. 32, No. 1-2, 145-158 (1997; Zbl 0890.39024)] for the superstability of the Cauchy and Jensen functional equation almost everywhere. A theorem is also proved concerning the superstability of the isometry equation in inner product spaces. This implies a new characterization of the property: The isometry equation is superstable in the integral norm. The reader is referred to the book of \textit{D. H. Hyers}, \textit{G. Isac} and \textit{Th. M. Rassias} [Stability of functional equations in several variables (1998; Zbl 0907.39025)] for several results and a large list of references concerning stability of functional equations.
scientific article; zbMATH DE number 1320610