Fixed Points and Stability of an Additive Functional Equation of $n$-Apollonius Type in $C^{*}$-Algebras
Fridoun Moradlou, Hamid Vaezi, and Choonkil Park
Source: Abstr. Appl. Anal. Volume 2008 (2008), 13 pages.
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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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1234298988
Digital Object Identifier: doi:10.1155/2008/672618
Mathematical Reviews number (MathSciNet):
MR2439255
Zentralblatt MATH identifier:
1159.47032
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