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SUPERSTABILITY OF MULTIPLICATIVE LINEAR MAPPINGS
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 Title & Authors
SUPERSTABILITY OF MULTIPLICATIVE LINEAR MAPPINGS
Anjidani, Ehsan; Ansari-Piri, Esmaeil;
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 Abstract
Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f : A B, in the sense of Rassias, is an algebra homomorphism.
 Keywords
stability of functional equation;superstability;algebra homomorphism;
 Language
English
 Cited by
 References
1.
R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), no. 2, 589-597. crossref(new window)

2.
D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397. crossref(new window)

3.
J. Brzdek and A. Pietrzyk, A note on stability of the general linear equation, Aequationes Math. 75 (2008), no. 3, 267-270. crossref(new window)

4.
S. Czerwik, Stability of Functional Equations of Hyers-Ulam-Rassias Type, Hadronic Press Inc., Palm Harbor, Florida, 2003.

5.
M. Eshaghi Gordji, Stability of an additive-quadratic functional equation of two variables in F-spaces, J. Nonlinear Sci. Appl. 2 (2009), no. 4, 251-259.

6.
G. L. Forti, Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations, J. Math. Anal. Appl. 295 (2004), no. 1, 127-133. crossref(new window)

7.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. crossref(new window)

8.
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. crossref(new window)

9.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998.

10.
A. Najati and C. Park, Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$-algebras, J. Nonlinear Sci. Appl. 3 (2010), no. 2, 123-143.

11.
C. Park, On an approximate automorphism on a $C^{*}$-algebra, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1739-1745. crossref(new window)

12.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. crossref(new window)

13.
S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.