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On the Stability of the Linear Mapping in Banach Spaces
Themistocles M. Rassias
Proceedings of the American Mathematical Society
Vol. 72, No. 2 (Nov., 1978), pp. 297-300
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2042795
Page Count: 4
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Let $E_1, E_2$ be two Banach spaces, and let $f: E_1 \rightarrow E_2$ be a mapping, that is "approximately linear". S. M. Ulam posed the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". The purpose of this paper is to give an answer to Ulam's problem.
Proceedings of the American Mathematical Society © 1978 American Mathematical Society