Stability of the Jensen-type functional equation in $$C^{\ast}$$-algebras: a fixed point approach.(English)Zbl 1167.39020

Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in $$C^{\ast }$$-algebras and Lie $$C^{\ast }$$-algebras and also of derivations on $$C^{\ast }$$-algebras and Lie $$C^{\ast }$$-algebras for the Jensen-type functional equation $$f((x+y)/2)+f((x - y)/2)=f(x)$$.

MSC:

 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 46L57 Derivations, dissipations and positive semigroups in $$C^*$$-algebras
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