一般可加性柯西方程的稳定性——不动点方法

The Stability of Generalized Additive Cauchy Equations-fixed Point Method

Jung利用直接法研究了一般可加性柯西方程f(x_0+∑mj=1a_jx_j)∑mi=1b_if∑mj=1aijxij)的稳定性,其中E_1是复赋范线性空间,E_2是复Banach空间,f是E_1到E_2的映射,利用不动点方法证明一般可加性柯西方程在复Banach空间上的稳定性。

Jung used the direct method to investigate the stability problem for a generalized additive Cauchym m m functional equation f（x0＋∑ajxj）=∑bif（∑aijxj） , where Ex is a complex normed space, E2 is a com-plex Banach space and f is a mapping from Ex to E2. In this work, the stability of the generalized additiveCauchy equation was obtained by the fixed point method in complex Banach space.