Abstract
Many applied problems (such as the intensity-modulated radiation therapy) can mathematically be formulated as the split feasibility problem and/or a fixed point problem. Iterative algorithms for solving the split feasibility problem and fixed point problem have therefore been extensively studied in the literature. In this paper we study the analytical methods for the split feasibility problem and fixed point problem. We introduce a new modified extragradient method involving with the regularization technique for the split feasibility problem and fixed point problem. Under some mild conditions, we prove that the suggested algorithm converges strongly to the minimum-norm common solution of the split feasibility problem and fixed point problem.