A strong convergence theorem for an iterative method for solving the multiple-sets split feasibility problem in Hilbert spaces
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Abstract: There are many iterative methods for solving the multiple-sets split feasibility problem involving step sizes that depend on the norm of a bounded linear operator F. The implementation of such algorithms is usually difficult to handle with because one haas to compute the norm of the operator F. In this talk, we introduce a new iterative algorithm for approximating a solution of a class of multiple-sets split feasibility problem without prior knowledge of operator norms. Strong convergence of the iterative process is proved. Then, we recapitulate the two methods for this class of problem which were given by Nguyen Buong (Iterative algorithms for the multiple-sets split feasibility problem in Hilbert spaces, Numer. Algor. 76 (2017), 783–798) and by Tran Viet Anh (A parallel method for variational inequalities with the multiple-sets split feasibility problem constraints, J. Fixed Point Theory Appl. 19 (2017), 2681–2696). A numerical example is given to illustrate the proposed iterative algorithm and compare it with the methods of Buong and Anh.