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Mann, W. (1953) Mean Value Methods in Iteration. Proceedings of the American Mathematical Society, 4, 506-510. http://dx.doi.org/10.1090/S0002-9939-1953-0054846-3
has been cited by the following article:
TITLE: A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces
AUTHORS: Akuchu Besheng George, Celestin Akwumbuom Nse
KEYWORDS: Demicontractive Maps, Mann Iterative Sequence, Strong Convergence, Monotonicity, Hilbert Spaces
JOURNAL NAME: Applied Mathematics, Vol.5 No.15, August 5, 2014
ABSTRACT: Letbe a real Hilbert space andCbe a nonempty closed convex subset of H. Let T : C→Cbe a demicontractive map satisfying〈Tx, x〉≥‖x‖2 for allx∈ D (T). Then the Mann iterative sequence given byxn + 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.
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