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

Rassias, John Michael

Discuss. Math. 7, 193-196 (1985).

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

Keywords:

approximately linear; Ulam Problem; conditions in order for a linear mapping near an approximately; linear mapping to exist; conditions in order for a linear mapping near an approximately linear mapping to exist