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Fixed points of multimaps which are not necessarily nonexpansive
Fixed Point Theory and Applications volume 2005, Article number: 286519 (2005)
Let be a nonempty closed bounded convex subset of a Banach space whose characteristic of noncompact convexity is less than and a continuous - -contractive map (which is not necessarily nonexpansive) from to satisfying an inwardness condition, where is the family of all nonempty compact convex subsets of . It is proved that has a fixed point. Some fixed points results for noncontinuous maps are also derived as applications. Our result contains, as a special case, a recent result of Benavides and Ramírez (2004).
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Shahzad, N., Lone, A. Fixed points of multimaps which are not necessarily nonexpansive. Fixed Point Theory Appl 2005, 286519 (2005). https://doi.org/10.1155/FPTA.2005.169