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ON THE EQUIVALENCE PRINCIPLE FOR CONTRACTIVE MAPPINGS
作者姓名:Ding  Xieping
作者单位:Sichuan Teacher's
摘    要:The main result is:Theorem 1.Let T be a continuous selfmapping of a complete metric space(X,d)andhave the unique fixed point property.If there exists n:X→N(the set of all positive integers)which is locally bounded such that for each x∈X and for all r∈N,r≥n(x),D(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),orD(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),where(?),and(?)are contractive gauge functions,then(a)T has a unique fixed point x~*;(b)For each x∈X,T~nx→x~* as n→∞;(e)There exists a neighborhood U(x~*)of x~* such that(?)T~n(U(x~*))={x~*};(d)x~*is stable;(e)For any given C∈(0,1)there exists a metric d~* topologically equivalent to d suchthat T is a Banach contraction under d~* with Lipschitz constant C.By Theorem 1 it is shown that many contractive type mappings defined in1—26]aretopologically equivalent to each other.

收稿时间:1981/11/2 0:00:00

ON THE EQUIVALENCE PRINCIPLE FOR CONTRACTIVE MAPPINGS
Ding Xieping.ON THE EQUIVALENCE PRINCIPLE FOR CONTRACTIVE MAPPINGS[J].Chinese Annals of Mathematics,Series B,1984,5(2):145-152.
Authors:Ding Xieping
Institution:Sichuan Teacher''s College
Abstract:
Keywords:
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