Stability of the Jensen-Type Functional Equation in C∗-Algebras: A Fixed Point Approach

Abstract

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$f\left(\left(x+y\right)/2\right)+f\left(\left(x-y\right)/2\right)=f\left(x\right)$.