A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces

• 作者: Akuchu Besheng George Celestin Akwumbuom Nse
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Demicontractive MAPS MANN Iterative Sequence Strong Convergence MONOTONICITY HILBERT Spaces
• 年，卷（期）: 2014,（15）
• 页码范围: 2195-2198
• 页数: 4页
• 分类号: O1

摘要

Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.