設X為賦距線性空間，KC(X)為X上所有非空緊緻的凸子集所成的集合，而א為KC(X).的子集，且T:א→KC(X)為非擴張映射。設{Xn}為א上的序列且{tn}為實序列，滿足下列：
(i)運算式略
(ii)運算式略
若{Xn}為有異，則limh(TXn,Xn)=0.
上述定理推廣了石川氏的結果。
Let X be a metric linear space, KC(X) is the collection of all nonempty, compact, convex subsets of X and א be a subset of KC(X). Suppose that T:א→KC(X) be a noncxpansive mapping. Given a sequence [Xn] in א and a recl scquences {tn} satisfying
(i) 運算式略
(ii)運算式略
If {Xn} is bounded then lim h(THn, Xn)=0.
The theorem generalize the result obtained by Ishikawa.
