Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
نویسندگان
چکیده
منابع مشابه
Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
and Applied Analysis 3 Very recently, Qin et al. 16 proposed the composite Halpern type iterative scheme in a uniformly smooth Banach space as follows: x0 x, u ∈ C, zn γnxn ( 1 − γn ) Txn, yn βnxn ( 1 − βn ) Tzn, xn 1 αnu 1 − αn yn, n ≥ 0, 1.6 and showed strong convergence of the sequence {xn} generated by 1.6 under the following control conditions: i ∑∞ n 0αn ∞; ii limn→∞αn 0, limn→∞βn 0 and 0...
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A mapping T : C → C is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We denote by Fix T {x ∈ C : Tx x} the set of fixed points of T . In the last ten years, many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see, e.g., 1–18 . An explicit iterative process was initially introduced, in 1967, by Halpern 3 i...
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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 pr...
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Viscosity approximation methods for nonexpansive mappings in CAT 0 spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subsetC of a CAT 0 spaceX. Suppose that the set Fix T of fixed points of T is nonempty. For a contraction f on C and t ∈ 0, 1 , let xt ∈ C be the unique fixed point of the contraction x → tf x ⊕ 1 − t Tx. We will show that if X is a CAT 0 space satisfy...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2009
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2009/573156