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http://dx.doi.org/10.14317/jami.2013.565

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)
Publication Information
Journal of applied mathematics & informatics / v.31, no.3_4, 2013 , pp. 565-575 More about this Journal
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).
Keywords
Pseudocontractive maps; fixed points; Ishikawa iteration; strong convergence; Hilbert spaces;
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