Strong Convergence of Composite Iterative Methods for Nonexpansive Mappings
نویسندگان
چکیده
Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C → C a contractive mapping (or a weakly contractive mapping), and T : C → C a nonexpansive mapping with the fixed point set F (T ) 6= ∅. Let {xn} be generated by a new composite iterative scheme: yn = λnf(xn)+(1−λn)Txn, xn+1 = (1−βn)yn+βnTyn, (n ≥ 0). It is proved that {xn} converges strongly to a point in F (T ), which is a solution of certain variational inequality provided the sequence {λn} ⊂ (0, 1) satisfies limn→∞ λn = 0 and ∑∞ n=0 λn = ∞, {βn} ⊂ [0, a) for some 0 < a < 1 and the sequence {xn} is asymptotically regular.
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