Displaying similar documents to “A remark on the approximate fixed-point property.”

Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

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...

Nonexpansive retracts in Banach spaces

Eva Kopecká, Simeon Reich (2007)

Banach Center Publications

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We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.

Proximal normal structure and relatively nonexpansive mappings

A. Anthony Eldred, W. A. Kirk, P. Veeramani (2005)

Studia Mathematica

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The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach space X and satisfy ∥ Tx-Ty∥ ≤ ∥ x-y∥ for all x ∈ A, y ∈ B. It is shown that if A and B are weakly compact and convex, and if the pair (A,B) has proximal normal structure, then a relatively nonexpansive mapping T: A ∪ B → A ∪ B satisfying (i) T(A) ⊆ B and T(B) ⊆ A, has a proximal point in...