HYERS-ULAM-RASSIAS STABILITY OF HOMOMORPHISMS IN QUASI-BANACH ALGEBRAS

Abstract

Let q be a positive rational number and n be a nonnegative integer. We prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following functional equation: Sigma(n)(i=1) f(Sigma(n)(j=1) q(x(i) - x(j)) + nf(Sigma(n)(j=1) qxi) = nq( (Sigma(n)(j=1) f(x(i)) This is applied to investigate isomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.