منابع مشابه
Convergence of approximating fixed points sets for multivalued nonexpansive mappings
Let K be a closed convex subset of a Hilbert space H and T : K ⊸ K a nonexpansive multivalued map with a unique fixed point z such that {z} = T (z). It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z.
متن کاملMore on minimal invariant sets for nonexpansive mappings
Minimal invariant sets for nonexpansive mappings share some singular geometrical properties. Here we present some seemingly unknown ones.
متن کاملProperties of Minimal Invariant Sets for Nonexpansive Mappings
In 1965 F. E. Browder [3] and D. Göhde [6] proved that each nonempty bounded and convex subset of a uniformly convex Banach space has fixed point property for nonexpansive mappings. Also in 1965 W. A. Kirk [8] came to the same conclusion for weakly compact convex subsets of any Banach space under additional assumption that the set has the so-called normal structure. This condition is much weake...
متن کاملFixed Points of Asymptotically Regular Nonexpansive Mappings on Nonconvex Sets
It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...
متن کاملOn Firmly Nonexpansive Mappings
It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-04053-7