Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras

Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras

We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(x−y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated b...

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Main Author: Choonkil Park
Format: Article
Language:English
Published: SpringerOpen 2007-08-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2007/50175
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spelling doaj-afa520bb93a348cdb60e6053657b6fd62020-11-25T01:03:38ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122007-08-01200710.1155/2007/50175Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach AlgebrasChoonkil ParkWe prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(x−y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).http://dx.doi.org/10.1155/2007/50175
collection DOAJ
language English
format Article
sources DOAJ
author Choonkil Park
spellingShingle Choonkil Park
Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
Fixed Point Theory and Applications
author_facet Choonkil Park
author_sort Choonkil Park
title Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
title_short Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
title_full Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
title_fullStr Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
title_full_unstemmed Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
title_sort fixed points and hyers-ulam-rassias stability of cauchy-jensen functional equations in banach algebras
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2007-08-01
description We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(x−y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).
url http://dx.doi.org/10.1155/2007/50175
work_keys_str_mv AT choonkilpark fixedpointsandhyersulamrassiasstabilityofcauchyjensenfunctionalequationsinbanachalgebras
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