Osilike, M.O. (2000) Strong and Weak Convergence of the Ishikawa Iteration Method for a Class of Nonlinear Equations. Bulletin of the Korean Mathematical Society, 37, 153-169.

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.