c_(0)上ε-范数可加映射的Hyers-Ulam稳定性

Hyers-Ulam Stability ofε-norm-additive Mappings on c_(0)

设Y为实Banach空间,ε≥0,映射f:c_(0)→Y为标准的ε-范数可加映射,即f(0)=0,且|‖f (x)+f(y)‖-‖x+y‖|≤ε,■x,y∈c_(0).本文证明对给定的δ>0,若f为δ-满射,则存在一个线性满等距U:c_(0)→Y,使得‖f (x)-U(x)‖≤3/2ε,■x∈c_(0).其中,常数3/2是最优的.

Let Y be a real Banach space,ε≥0,and let f:c_(0)→be a standardε-norm-additive mapping,i.e.,f(0)=0 and|‖f(x)+f(y)‖-‖x+y‖|≤g,■x,y∈c_(0).In this paper,we show that if f isδ-surjective for someδ>0,then there exists a linear surjective isometry U:c_(0)→Y such that‖f(x)-U(x)‖≤3/2ε,■x∈c_(0).The constant3/2 is optimal.