CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING

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PARK C.G.; SONG J.H.

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Journal Paper

Paper Information

Journal: Bulletin of the Iranian Mathematical Society Year:2009 | Volume:35 | Issue:2 Page(s): 143-162

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Title

CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING

Author(s)

PARK C.G. | SONG J.H. | Issue Writer Certificate

Keywords

CAUCHY-RASSIAS STABILITY

C*C*-ALGEBRA HOMOMORPHISM

POISSON C*-ALGEBRA HOMOMORPHISM

POISSON BANACH MODULE OVER POISSON C*-ALGEBRA

POISSON JC*-ALGEBRA HOMOMORPHISM

Abstract

Let X and Y be vector spaces. We show that a mapping f : X ®Y satisfies the functional equation,
f (x1 +S2dj=2(-1)j xj)-f (x1+S2dj=2(-1)j-1xj)=2S2dj=2 (-1)j (xj)if and only if the mapping f : X ® Y is Cauchy additive, and prove the CAUCHY-RASSIAS STABILITY of the above functional equation in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, we show that every almost homomorphism h A®B of A into B is a homomorphism when h(2nuy) = h(2nu)h(y) or h(2nu°y) = h(2nu) o h(y), for all unitaries u Î A, all y Î A, and n = 0, 1, 2, Moreover, we prove the CAUCHY-RASSIAS STABILITY of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.

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APA: Copy

PARK, C.G., & SONG, J.H.. (2009). CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 35(2), 143-162. SID. https://sid.ir/paper/569075/en

Vancouver: Copy

PARK C.G., SONG J.H.. CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2009;35(2):143-162. Available from: https://sid.ir/paper/569075/en

IEEE: Copy

C.G. PARK, and J.H. SONG, “CAUCHY-RASSIAS STABILITY OF LINEAR MAPPINGS IN BANACH MODULES ASSOCIATED WITH A GENERALIZED JENSEN TYPE MAPPING,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 35, no. 2, pp. 143–162, 2009, [Online]. Available: https://sid.ir/paper/569075/en

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