GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS
Copyright policy )GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS
The generalized Hyers-Ulam-Rassias stability of the functional equation \[ 2^nf\biggl({{x_1+\dots+x_{2^n}}\over{2^n}}\biggr)=\sum_{i=1}^{2^n}f(x_i)\tag{1} \] is proved in Banach modules over a~unital \(C^{\ast}\)-algebra. The Hyers-Ulam-Rassias stability of algebra homomorphisms between Banach algebras associated with the functional equation (1) is also proved.
Linear operators on Banach algebras, General theory of \(C^*\)-algebras, Banach module over \(C^{\ast}\)-algebra, Jensen's functional equation, Stability, separation, extension, and related topics for functional equations, Functional equations for functions with more general domains and/or ranges, Hyers-Ulam-Rassias stability, approximate algebra homomorphism
Linear operators on Banach algebras, General theory of \(C^*\)-algebras, Banach module over \(C^{\ast}\)-algebra, Jensen's functional equation, Stability, separation, extension, and related topics for functional equations, Functional equations for functions with more general domains and/or ranges, Hyers-Ulam-Rassias stability, approximate algebra homomorphism
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