Endpoints of set-valued contractions in metric spaces
(Citations: 3)
Suppose (X,d) be a complete metric space, and suppose F:X→CB(X) be a set-valued map satisfies H(Fx,Fy)≤ψ(d(x,y)), for eachx,y∈X, where ψ:[0,∞)→[0,∞) is upper semicontinuous, ψ(t)t for each t>0 and satisfies lim inft→∞(t−ψ(t))>0. Then F has a unique endpoint if and only if F has the approximate endpoint property.