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Let be a nonexpansive multivalued mapping, then the set of fixed points of is nonempty.
Let be a nonempty closed convex bounded subset of a uniformly convex Banach space, and let be a nonexpansive multivalued mapping.
Let C be a nonempty closed convex subset of a real Hilbert space H. Let T : C → K ( C ) be a nonexpansive multivalued mapping.
Let C be a closed convex subset of a real Hilbert space H. Let T : C → C B ( C ) be a nonexpansive multivalued mapping.
Let C be a nonempty closed convex subset of a real Hilbert space H. Let (S : Cto mathit{CB}(C)) be a nonexpansive multivalued mapping with (F(S neemptyset) and (Sp={p}) for each (pin F(S)).
Let (T: K to mathit{CB}(K)) be a nonexpansive multivalued mappings such that (operatorname{Fix}(T) neqphi) and for which (T(p) = {p}) for each (p inoperatorname{Fix}(T)).
Similar(53)
However, if S is a nonexpansive multivalued mapping and (Sp={p}) for each (pin F(S)), then (F(S)) is always closed and convex as the following result shows.
Let be a nonempty bounded closed convex subset of a uniformly Banach space, and let, and be a nonexpansive mapping and a multivalued nonexpansive mapping, respectively.
A multivalued mapping is said to be a nonexpansive if (1.2).
Let T i : K → P ( K ), i = 1, 2 be a multivalued mapping and T T i be a nonexpansive mapping, let S i : K → K, i = 1, 2 be a nonexpansive mapping.
Let T i : K → P ( K ), i = 1, 2 be a multivalued mapping and T T i, i = 1, 2 be a nonexpansive mapping.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com