Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STRONG CONVERGENCE OF A NEW ITERATIVE ALGORITHM FOR AVERAGED MAPPINGS IN HILBERT SPACES

  • Yao, Yonghong (Department of Mathematics, Tianjin Polytechnic University) ;
  • Zhou, Haiyun (Department of Mathematics, Shijiazhuang Mechanical Engineering College) ;
  • Chen, Rudong (Department of Mathematics, Tianjin Polytechnic University)
  • Received : 2009.09.10
  • Accepted : 2009.10.18
  • Published : 2010.05.30
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Abstract

Let H be a real Hilbert space. Let T : $H\;{\rightarrow}\;H$ be an averaged mapping with $F(T)\;{\neq}\;{\emptyset}$. Let {$\alpha_n$} be a real numbers in (0, 1). For given $x_0\;{\in}\;H$, let the sequence {$x_n$} be generated iteratively by $x_{n+1}\;=\;(1\;-\;{\alpha}_n)Tx_n$, $n\;{\geq}\;0$. Assume that the following control conditions hold: (i) $lim_{n{\rightarrow}{\infty}}\;{\alpha}_n\;=\;0$; (ii) $\sum^{\infty}_{n=0}\;{\alpha}_n\;=\;{\infty}$. Then {$x_n$} converges strongly to a fixed point of T.

Keywords

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