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

Xiaolong Qin ; Yongfu Su ; Meijuan Shang

Open Mathematics, Tome 5 (2007), p. 345-357 / Harvested from The Polish Digital Mathematics Library

Résumé

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 n, α′ n, α″ n ≤ 1 − ∈ for all n ∈ N and some ∈ > 0. Starting from arbitrary x 1 ∈ K define the sequence x n by zn=P(αn''T3(PT3)n-1xn+(1-αn'')xn),yn=P(αn'T2(PT2)n-1zn+(1-αn')xn),xn+1=P(αnT1(PT1)n-1yn+(1-αn)xn). (i) If the dual E* of E has the Kadec-Klee property then x n converges weakly to a common fixed point p ∈ F; (ii) If T satisfies condition (A′) then x n converges strongly to a common fixed point p ∈ F.

Détail

Publié le : 2007-01-01

Zbl 1140.47055

EUDML-ID : urn:eudml:doc:269414

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