Further investigation into split common fixed point problem for demicontractive operators

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• 作者：Yekini Shehu ; Oluwatosin T. Mewomo
• 关键词：Demicontractive mappings ; split common fixed point problems ; iterative scheme ; strong convergence ; Hilbert spaces
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：32
• 期：11
• 页码：1357-1376
• 全文大小：278 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617
• 卷排序：32

文摘

Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.