Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces.
Jung, Jong Soo, Park, Jong Yeoul, Park, Jong Seo (1997)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “Normal structure and common fixed point properties for semigroups of nonexpansive mappings in Banach spaces.”
Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces.
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It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.
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Andrzej Wiśnicki (2011)
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We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
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Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces
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Xiaolong Qin, Yongfu Su, Meijuan Shang (2007)
Open Mathematics
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Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: K → E be asymptotically nonexpansive mappings with k n, l n and j n. [1, ∞) such that Σn=1∞(k n − 1) < ∞, Σn=1∞(l n − 1) < ∞ and Σn=1∞(j n − 1) < ∞, respectively and F nonempty, where F = x ∈ K: T 1x = T 2x = T 3 x = xdenotes the common fixed points set of T 1, T 2 and T 3. Let α n, α′ n and α″ n be real sequences in (0, 1) and ∈ ≤ α...