Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings
نویسندگان
چکیده
منابع مشابه
Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings
Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori 2001 and Zhang and Su 2007 as special cases. We also apply our method to find a common element to the set o...
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The purpose of this paper is to study weak and strong convergence of a new implicit iteration process to a common fixed point for a finite family of nonexpansive mappings in a uniformly convex Banach space. The results obtained in this paper extend and improve the corresponding results of [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of none...
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متن کاملStrong Convergence Theorems for a Finite Family of Nonexpansive Mappings
Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2008
ISSN: 1687-1812
DOI: 10.1155/2008/732193