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.