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Abstract and Applied Analysis
Volume 2008, Article ID 672618, 13 pages
http://dx.doi.org/10.1155/2008/672618
Research Article

Fixed Points and Stability of an Additive Functional Equation of 𝑛-Apollonius Type in πΆβˆ—-Algebras

1Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
2Department of Mathematics, Hanyang University, Seoul 133–791, South Korea

Received 22 April 2008; Revised 11 June 2008; Accepted 16 July 2008

Academic Editor: John Rassias

Copyright Β© 2008 Fridoun Moradlou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of πΆβˆ—-algebra homomorphisms and of generalized derivations on πΆβˆ—-algebras for the following functional equation of Apollonius type _𝑛𝑖=1_𝑓(𝑧_π‘₯𝑖)=_(1/𝑛)___1_𝑖<𝑗_𝑛_𝑓(π‘₯𝑖+π‘₯𝑗)+𝑛𝑓(𝑧_(1/𝑛2)_𝑛𝑖=1_π‘₯𝑖).