An asymptotically nonexpansive commutative semigroup with no fixed points
نویسندگان
چکیده
منابع مشابه
Viscosity Approximation Methods for Fixed Points of Asymptotically Nonexpansive Semigroup in Banach Space
In this paper, under the framework of Banach space with uniformly Gateauxdifferentiable norm and uniform normal structure, we use the existence theorem of fixed points of Gang Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive semigroup. We get the convergence theorems.
متن کاملcommon fixed points of jointly asymptotically nonexpansive mappings
a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...
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 کاملApproximating Fixed Points of Total Asymptotically Nonexpansive Mappings
The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...
متن کاملCommon Fixed Points of Commutative Semigroups of Nonexpansive Mappings
Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0831397-9