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GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS

  • Published : 2002.08.01

Abstract

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

Keywords

stability;Jensen's functional equation;Banach module over $C^{*}$-algebra;approximate algebra homomorphism

References

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  5. Duke Math. J. v.16 Approximately isometric and multiplicative transformations on continuous function rings D. G. Bourgin https://doi.org/10.1215/S0012-7094-49-01639-7
  6. Math. Scand. v.57 Means and convex combinations of unitary operators R. Kadison;G. Pedersen

Cited by

  1. On the stability of Euler–Lagrange type cubic mappings in quasi-Banach spaces vol.332, pp.2, 2007, https://doi.org/10.1016/j.jmaa.2006.11.024
  2. C *-Ternary 3-Homomorphisms on C *-Ternary Algebras vol.66, pp.1-2, 2014, https://doi.org/10.1007/s00025-014-0365-7
  3. A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS vol.47, pp.5, 2010, https://doi.org/10.4134/BKMS.2010.47.5.987
  4. Asymptotic behavior of the extended Jensen equation vol.46, pp.1, 2009, https://doi.org/10.1556/SScMath.2008.1077