Hyers-Ulam Stability of ε-norm-additive Mappings on c0
Let Y be a real Banach space,ε ≥ 0,and let f:c0 → Y be a standardε-norm-additive mapping,i.e.,f(0)=0 and |‖f(x)+f(y)‖-‖x+y‖| ≤ ε,Vx,y ∈ c0.In this paper,we show that if f is δ-surjective for some δ＞0,then there exists a linear surjective isometry U:c0 Y such that ‖f(x)-U(x)‖ ≤ 3/2ε,∀ x ∈ c0.The constant 3/2 is optimal.
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