Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STRONG CONVERGENCE OF A MODIFIED ISHIKAWA ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDOCONTRACTIVE MAPPINGS

  • Osilike, M.O. (Department of Mathematics, University of Nigeria) ;
  • Isiogugu, F.O. (Department of Mathematics, University of Nigeria) ;
  • Attah, F.U. (Department of Mathematics, University of Nigeria)
  • Received : 2012.09.02
  • Accepted : 2012.10.11
  • Published : 2013.05.30
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Abstract

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

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References

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