Abstract
In this note, we prove a generalization of Hyers’ theorem on the stability of approximately additive mapping and a generalization of Badora’s theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam’s problem.
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This work is partly supported by the National Natural Science Foundation of China(19771056)
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Zhang, D.H., Cao, H.X. Stability of Functional Equations in Several Variables. Acta Math Sinica 23, 321–326 (2007). https://doi.org/10.1007/s10114-005-0862-4
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DOI: https://doi.org/10.1007/s10114-005-0862-4