Publication Date:
1980-01-01
Description:
LetSbe a subset of a metric spaceXand letB(X)be the class of all nonempty bounded subsets ofXwith the Hausdorff pseudometricH. A mappingF:S→B(X)is a directional contraction iff there exists a realα∈[0,1)such that for eachx∈Sandy∈F(x),H(F(x),F(z))≤αd(x,z)for eachz∈[x,y]∩S, where[x,y]={z∈X:d(x,z)+d(z,y)=d(x,y)}. In this paper, sufficient conditions are given under which such mappings have a fixed point.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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