A STRONG CONVERGENCE OF A MODIFIED KRASNOSELSKII‐MANN METHOD FOR NON‐EXPANSIVE MAPPINGS IN HILBERT SPACES
نویسندگان
چکیده
منابع مشابه
Strong Convergence Theorems of Modified Mann Iterative Process for Nonexpansive Mappings in Hilbert Spaces
The purpose of this article is to modify normal Mann’s iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.
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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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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2010
ISSN: 1392-6292,1648-3510
DOI: 10.3846/1392-6292.2010.15.265-274