Fixed Points and Stability of an Additive Functional Equation of n -Apollonius Type in C ∗ -Algebras

Fridoun Moradlou; Hamid Vaezi; Choonkil Park

doi:10.1155/2008/672618

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Home > Journals > Abstr. Appl. Anal. > Volume 2008 > Article

2008 Fixed Points and Stability of an Additive Functional Equation of

n

-Apollonius Type in

C^{*}

-Algebras

Fridoun Moradlou, Hamid Vaezi, Choonkil Park

Abstr. Appl. Anal. 2008: 1-13 (2008). DOI: 10.1155/2008/672618

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Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of ${C}^{\ast}$ -algebra homomorphisms and of generalized derivations on ${C}^{\ast}$ -algebras for the following functional equation of Apollonius type ${\sum }_{i=1}^{n}f(z-{x}_{i})=-(1/n){\sum }_{1\leq i< j\leq n}f({x}_{i}+{x}_{j})+nf(z-(1/{n}^{2}){\sum }_{i=1}^{n}{x}_{i})$ .

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Fridoun Moradlou. Hamid Vaezi. Choonkil Park. "Fixed Points and Stability of an Additive Functional Equation of $n$ -Apollonius Type in $C^{*}$ -Algebras." Abstr. Appl. Anal. 2008 1 - 13, 2008. https://doi.org/10.1155/2008/672618