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Proceedings of the American Mathematical Society

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On the stability of the linear mapping in Banach spaces


Author: Themistocles M. Rassias
Journal: Proc. Amer. Math. Soc. 72 (1978), 297-300
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1978-0507327-1
MathSciNet review: 507327
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Abstract: Let $ {E_1},{E_2}$ be two Banach spaces, and let $ f:{E_1} \to {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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507327-1
Keywords: Approximately linear mapping
Article copyright: © Copyright 1978 American Mathematical Society