Publication Date:
1983-01-01
Description:
LetXandYbe complete metric spaces withYmetrically convex, letD⊂Xbe open, fixu0∈X, and letd(u)=d(u0,u)for allu∈D. Letf:X→2Ybe a closed mapping which maps open subsets ofDonto open sets inY, and supposefis locally expansive onDin the sense that there exists a continuous nonincreasing functionc:R+→R+with∫+∞c(s)ds=+∞such that each pointx∈Dhas a neighborhoodNfor whichdist(f(u),f(v))≥c(max{d(u),d(v)})d(u,v)for allu,v∈N. Then, giveny∈Y, it is shown thaty∈f(D)iff there existsx0∈Dsuch that forx∈XD,dist(y,f(x0))≤dist(u,f(x)). This result is then applied to the study of existence of zeros of (set-valued) locally strongly accretive andϕ-accretive mappings in Banach spaces
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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