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Using the fixed point method, we prove the generalized Hyers-Ulam stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following functional equation of Apollonius type ∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi)

abstract and applied analysis

Fixed Points and Stability of an Additive Functional Equation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-Apollonius Type in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math>-Algebras

Fixed Points and Stability of an Additive Functional Equation ofn-Apollonius Type inC∗-Algebras