ISOMORPHISMS IN QUASI-BANACH ALGEBRAS

Title & Authors
ISOMORPHISMS IN QUASI-BANACH ALGEBRAS
Park, Choon-Kil; An, Jong-Su;

Abstract
Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $\small{2f(\frac{x+y}{2}+z)}$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.
Keywords
Cauchy-Jensen functional equation;isomorphism;isometry;derivation;quasi-Banach algebra;
Language
English
Cited by
1.
PERTURBATIONS OF HIGHER TERNARY DERIVATIONS IN BANACH TERNARY ALGEBRAS,;;

대한수학회논문집, 2008. vol.23. 3, pp.387-399
2.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS,;;

대한수학회보, 2010. vol.47. 1, pp.195-209
3.
ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS,;;

대한수학회보, 2011. vol.48. 5, pp.959-967
1.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 1
2.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 195
3.
Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras, Analysis in Theory and Applications, 2011, 27, 2, 109
4.
Stability of a Bi-Additive Functional Equation in Banach Modules Over aC⋆-Algebra, Discrete Dynamics in Nature and Society, 2012, 2012, 1
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