The Split Feasibility Problem Based On Class-(?)_α Operators

Bauschke and Combettes proposed the conception of (?) operators in Hilbert space in2001. Inspired by this, we introduce the conception of (?)α operators and we apply this new conception for solving the split feasibility problem (SFP). Our purpose is to deal with some well-known algorithms for solving SFP in a unified framework and to construct some new algorithms. We will consider the CQ iteration, Mann iteration and Takahashi iteration. Based on the Ta operators, we can treat these iterative schemes uniformly for solving more general SFP problems. By numerical experiments, we verify our algorithms efficiently in comparision with some well-known algorithms. The contents of the master thesis are arranged as follows:In Chapter1, we introduce the split feasibility problems and the fixed point prob-lems with corresponding iterative methods.In Chapter2, we introduce the orthogonal projection operators and the averaged operators and specially introduce the conceptions and properties of the class-Tα oper-ators.In Chapter3, based on the theory of the (?)a operators as well as CQ iteration, Mann iteration and Takahashi iteration, we propose some new algorithms for solving split feasibility problem (SFP) and prove the convergence results under certain condi-tions. We also extend our algorithms for solving the split common fixed point problem (SCFPP).In Chapter4, by numerical experiments, we verify our algorithms. We analyze the effect of the parameters of our methods on the computational efficiency. We also present the comparision of our algorithms with the well-known CQ iteration method.