Abstract
Let E 1 be a real normed vector space and E 2 a real Banach space. S. M. Ulam posed the problem: When does a linear mapping near an approximately linear mapping ƒ: E 1 ↦ E 2 exist? We give a new generalized solution to this problem. An example illustrates when the answer to this question is negative. The behaviour of bounded approximately additive mappings which do not satisfy Hyers-UIam stability is also investigated.
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