article
On the Stability of the Linear Mapping in Banach Spaces
Proceedings of the American Mathematical Society · 1978 · Vol. 72(2) · pp. 297–297
Themistocles M. Rassias✉(University of California, Berkeley)
Abstract
Let ${E_1},{E_2}$ be two Banach spaces, and let $f:{E_1} \to {E_2}$ be a mapping, that is âapproximately linear". S. M. Ulam posed the problem: âGive 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 Ulamâs problem.
Nonlinear Differential Equations Analysisadvanced mathematical theoriesFunctional Equations Stability ResultsBanach spaceMathematicsStability (learning theory)Order (exchange)Linear mapPure mathematicsComputer scienceEconomics
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On the behavior of mappings which do not satisfy Hyers-Ulam stability
Proceedings of the American Mathematical Society · 1992 · 407 citations
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