Abstract
Abstract In this paper, using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in C ∗ -algebras and Lie C ∗ -algebras and of derivations on C∗-algebras and Lie C∗-algebras for an m-variable additive functional equation. MSC:39A10, 39B52, 39B72, 46L05, 47H10, 46B03.
Highlights
1 Introduction and preliminaries The stability problem of functional equations originated from a question of Ulam [ ] concerning the stability of group homomorphisms: Let (G, ∗) be a group and let (G, d) be a metric group with the metric d(·, ·)
Given >, does there exist a δ( ) > such that if a mapping h : G → G satisfies the inequality d(h(x ∗ y), h(x) h(y)) < δ for all x, y ∈ G, there is a homomorphism H : G → G with d(h(x), H(x)) < for all x ∈ G ? If the answer is affirmative, we say that the equation of homomorphism H(x ∗ y) = H(x) H(y) is stable
In this paper, using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms and derivations in Lie C∗-algebras for the following additive functional equation: m m f mxi + xj + f i=
Summary
Introduction and preliminariesThe stability problem of functional equations originated from a question of Ulam [ ] concerning the stability of group homomorphisms: Let (G , ∗) be a group and let (G , , d) be a metric group with the metric d(·, ·). In this paper, using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms and derivations in Lie C∗-algebras for the following additive functional equation (see [ ]): m m f mxi + xj + f i=
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