STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II

NAJATI , ABBAS; PARK, CHOONKIL

doi:10.22436/jnsa.003.02.05

Geodesic

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STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II

NAJATI , ABBAS ¹ ; PARK, CHOONKIL ²

¹ Department of Mathematics Faculty of Sciences, University of Mohaghegh Ardabili , Ardabil,56199-11367, Iran
² Department of Mathematics Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea

Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 123-143.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Résumé

Let $X; Y$ be Banach modules over a $C^*$-algebra and let $r_1,..., r_n \in \mathbb{R}$ be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital $C^*$-algebra:

$\sum^n_{j=1}f(\frac{1}{2}\sum_{1\leq i\leq n;i\neq j}r_ix_i − \frac{1}{2}r_jx_j)+\sum^n_{i=1}r_if(x_i) = nf(\frac{1}{2}\sum^n_{i=1}r_ix_i) \qquad (0.1)$

We show that if $\sum^n_{i=1 }r_i\neq 0; r_i \neq 0; r_j \neq 0$ for some $1 \leq i j \leq n$ and a mapping $f : X \rightarrow Y$ satisfies the functional equation (0.1) then the mapping $f : X \rightarrow Y$ is additive. As an application, we investigate homomorphisms in unital $C^*$-algebras.

DOI : 10.22436/jnsa.003.02.05

Classification : 39B72, 46L05, 47B48
Keywords: Generalized Hyers-Ulam stability, generalized Euler-Lagrange type additive mapping, homomorphism in $C^*$-algebras.

Affiliations des auteurs :

NAJATI , ABBAS ¹ ; PARK, CHOONKIL ²

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NAJATI , ABBAS ; PARK, CHOONKIL . STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 123-143. doi : 10.22436/jnsa.003.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.02.05/

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