Iterative Algorithms for Nonexpansive Mappings
نویسندگان
چکیده
منابع مشابه
Iterative Algorithms for Nonexpansive Mappings
for all x, y ∈ C. We use F T to denote the set of fixed points of T , that is, F T {x ∈ C : Tx x}. Throughout the paper, we assume that F T / ∅. Construction of fixed points of nonlinear mappings is an important and active research area. In particular, iterative methods for finding fixed points of nonexpansive mappings have received a vast investigation; see 1–28 . It is well known that the Pic...
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Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F S ∩ F T / ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn 1 βnxn 1 − βn Syn, yn αnγ...
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The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...
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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...
متن کاملIterative Schemes for Fixed Point Computation of Nonexpansive Mappings
and Applied Analysis 3 Moreover, PC is characterized by the following properties: 〈 x − PCx, y − PCx 〉 ≤ 0, ∥ ∥x − y∥∥2 ≥ ‖x − PCx‖ ∥ ∥y − PCx ∥ ∥ 2 , 2.4 for all x ∈ H and y ∈ C. We also need other sorts of nonlinear operators which are introduced below. Let T : H → H be a nonlinear operator. a T is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ H. b T is firmly nonexpansive if 2T − I is n...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2008
ISSN: 1687-1820,1687-1812
DOI: 10.1155/2008/384629