STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE#br#
FUNCTIONAL EQUATION

doi:10.1016/S0252-9602(12)60094-0

Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (3): 1226-1238.doi: 10.1016/S0252-9602(12)60094-0

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STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE#br# FUNCTIONAL EQUATION

Ali Ebadian¹|Ismail Nikoufar¹|Themistocles M. Rassias²|Norouz Ghobadipour³

1. Department of Mathematics, Payame Noor University, PO Box 19395-3697 Tehran, Iran；
2. Department of Mathematics, National Technical University of Athens, Zografou, Campus 15780 Athens, Greece；
3. Department of Mathematics, Urmia University, Urmia, Iran

Received:2011-01-14 Revised:2011-02-15 Online:2012-05-20 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.

Key words: Hyers-Ulam-Rassias stability, Hilbert C*-module, generalized derivation fixed point

CLC Number:

39B52

Cite this article

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.

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http://121.43.60.238/sxwlxbB/EN/Y2012/V32/I3/1226

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[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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