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 and let . If and for all , then there is exactly one ring homomorphism such that for all . 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.