On a new approximation of approximately linear mappings by linear mappings.(English)Zbl 0592.46004

Assume A is a normed linear space, B is a Banach space, and $$f: A\to B$$ is a mapping ”approximately linear”. In this paper we solve the following Ulam Problem: ”Give conditions in order for a linear mapping near an approximately linear mapping to exist”.

MSC:

 46A32 Spaces of linear operators; topological tensor products; approximation properties 46B20 Geometry and structure of normed linear spaces 41A30 Approximation by other special function classes