Strong convergence of a self-adaptive method for the split feasibility problem in Banach spaces
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In signal processing and image reconstruction, the split feasibility problem (SFP) has been now investigated extensively because of its applications. A classical way to solve the SFP is to use Byrne’s CQ-algorithm. However, this method requires the computation of the norm of the bounded linear operator or the matrix norm in a finite-dimensional space. In this work, we aim to propose an iterative scheme for solving the SFP in the framework of Banach spaces. We also introduce a new way to select the step-size which ensures the convergence of the sequences generated by our scheme. We finally provide examples including its numerical experiments to illustrate the convergence behavior. The main results are new and complements many recent results in the literature.
KeywordsSplit feasibility problem strong convergence self-adaptive method optimization Banach space
Mathematics Subject Classification47H04 47H10 54H25
This research was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248. S. Suantai would like to thank Chiang Mai University. The research was carried out when the second author was an Alexander von Humboldt Postdoctoral Fellow at the Institute of Mathematics, University of Wurzburg, Germany. He is grateful to the Alexander von Humboldt Foundation, Bonn, for the fellowship and the Institute of Mathematics, Julius Maximilian University of Wurzburg, Germany, for the hospitality and facilities.
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