Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

• Published in: Acta mathematica Sinica. English series Vol. 32; no. 11; pp. 1357 - 1376
• Main Authors: Shehu, Yekini, Mewomo, Oluwatosin T.
• Format: Journal Article
• Language: English
• Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2016; Springer Nature B.V
• Subjects: Algorithms; Approximation; Codes; Convergence; Feasibility; Fixed points (mathematics); Hilbert space; Mapping; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Norms; Operators; Studies; Viscosity; split common fixed point problems; Demicontractive mappings; 47H09; Hilbert spaces; 47J05; iterative scheme; 47J25; 47H06; strong convergence
• ISSN: 1439-8516; 1439-7617
• DOI: 10.1007/s10114-016-5548-6

Our contribution in this paper is to propose an iterative algorithm which does not reqmre 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 Mgorithms 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 Mgorithm 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.