Jordan映射的超稳定性

The superstability of Jordan mappings

基于ε-同态,Jordan映射,ε-近似Jordan映射,强ε-近似Jordan映射,ε-准Jordan映射的概念,给出了ε-近似Jordan映射超稳定性的定义.在此基础上给出映射超稳定性的一些充分条件,以及在某个适当条件下ε-近似Jordan映射是保k次方的(k∈N+).

Based on the conceptions of Jordan mapping, s-approximate Jordan mapping, strong ε-Jordan mapping, ε-near Jordan mapping, the definition of superstability of ε-approximate Jordan mapping is given. And then, some sufficient conditions for the superstabilities, and ε-approximate Jordan mapping holds k power under some suitable conditions are obtained,where k is a positive integer number.