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.

In this paper, we give generalization of Hyers' theorem on the stability of approximately additive mapping and a generalization of Badora's theorem on approximate ring homomorphism. We also obtain a more general stability theorem, which gives 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 stability of functional equations connected with S. M. Ulam's problem.

in this paper ,we give a generalization of Hyers-ulam stability result of the approximately additive mapping on a restricted domain.Some applications are also given.

首先引入r重正交小波和多尺度分析的概念,然后讨论了r重多尺度分析中闭线性子空间和尺度函数的性质,最后在最一般的情况下,给出了r重正交小波的存在性证明.

A generalization of classical Neumann lemma are proved and some applications to the study of perturbations of operators,Bessel sequences and frames are also given.