Endpoints of set-valued contractions in metric spaces Original Research Article

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