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On approximate ring homomorphisms. (English) Zbl 1014.39020

The subject is stability of Hyers-Ulam type and of Rassias type of ring homomorphisms from a ring into a Banach-algebra .

The main result of the paper on Hyers-Ulam stability is: Let f: and let ε,δ>0. If f(x+y)-f(x)-f(y)ε and f(xy)-f(x)f(y)δ for all x,y, then there is exactly one ring homomorphism h: such that f(x)-h(x)ε for all x. This extends Theorem 5 of D. G. Bourgin’s paper [Duke Math. J. 16, 385–397 (1949; Zbl 0033.37702)].

The author modifies his proof to obtain a similar result about stability of Rassias type of ring homomorphisms in case is a normed algebra.

39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges