Acta mathematica scientia, Series B >
STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE#br# FUNCTIONAL EQUATION
Received date: 2011-01-14
Revised date: 2011-02-15
Online published: 2012-05-20
In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equation
rf(x + y/r ) + sg(x − y/s ) = 2h(x)
for r, s∈R\ {0} on Hilbert C*-modules, where f, g, and h are mappings from a Hilbert C*-module M to M.
Ali Ebadian , Ismail Nikoufar , Themistocles M. Rassias , Norouz Ghobadipour . STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE#br# FUNCTIONAL EQUATION[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1226 -1238 . DOI: 10.1016/S0252-9602(12)60094-0
[1] Amyari M, Moslehian M S. Hyers-Ulam-Rassias stability of derivations on Hilbert C*-modules. Contem-porary Math, 2007, 427: 31–39
[2] Aoki T. On the stability of the linear transformation in Banach spaces. J Math Soc Japan, 1950, 2: 64–66
[3] Cadariu L, Radu V. On the stability of the Cauchy functional equation: a fixed point approach. Grazer Math Ber, 2004, 346: 43–52
[4] Czerwik S. Stability of functional equations of Ulam-Hyers-Rassias type. Palm Harbor, Florida: Hadronic Press, 2003
[5] Ebadian A, Ghobadipour N, Eshaghi Gordji M. A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C*-ternary algebras. J Math Phys, 2010, 103508, 51.
[6] Eshaghi Gordji M, Rassias J M, Ghobadipour N. Generalized Hyers–Ulam stability of generalized (n, k)-derivations. Abstract and Applied Analysis, 2009: 1–8
[7] Eshaghi Gordji M, Ghobadipour N. Nearly generalized Jordan derivations. Math Slovaca, 2011, 61(1): 1–8
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