Displaying similar documents to “Fixed-point theorems for mapping defined on unbounded sets in Banach spaces”

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...

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...