STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II
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Authors
ABBAS NAJATI
- Department of Mathematics Faculty of Sciences, University of Mohaghegh Ardabili , Ardabil,56199-11367, Iran.
CHOONKIL PARK
- Department of Mathematics Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea.
Abstract
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.
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ISRP Style
ABBAS NAJATI, CHOONKIL PARK, STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II, Journal of Nonlinear Sciences and Applications, 3 (2010), no. 2, 123 - 143
AMA Style
NAJATI ABBAS, PARK CHOONKIL, STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II. J. Nonlinear Sci. Appl. (2010); 3(2):123 - 143
Chicago/Turabian Style
NAJATI , ABBAS, PARK, CHOONKIL. "STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II." Journal of Nonlinear Sciences and Applications, 3, no. 2 (2010): 123 - 143
Keywords
- Generalized Hyers-Ulam stability
- generalized Euler-Lagrange type additive mapping
- homomorphism in \(C^*\)-algebras.
MSC
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