A new sufficient condition for the strong convergence of Halpern type iterations
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摘要
The aim of this work is to give a new sufficient condition of the strong convergence of the Halpern type iteration for a non-expansive self-mapping defined on a Banach space with a uniformly Gâteaux differentiable norm. Several examples satisfying our condition are presented. Our results not only remove the restriction of the space with the fixed point property for non-expansive self-mappings, but also get rid of the dependence on the convergence of the implicit anchor-like continuous path zt in the proof.
论文关键词:Non-expansive mappings,Halpern type iteration,Uniformly Gâteaux differentiable norm
论文评审过程:Available online 21 September 2007.
论文官网地址:https://doi.org/10.1016/j.amc.2007.09.010