Three-Step Projective Methods for Solving the Split Feasibility Problems

Abstract

In this paper, we focus on studying the split feasibility problem (SFP) in Hilbert spaces. Based on the CQ algorithm involving the self-adaptive technique, we introduce a three-step iteration process for approximating the solution of SFP. Then, the convergence results are established under mild conditions. Numerical experiments are provided to show the efficiency in signal processing. Some comparisons to various methods are also provided in this paper.

Convex minimization problems based on an accelerated fixed point algorithm with applications to image restoration problems

“…In the real word, fixed point theory have been applied to many branches of applied analysis; see, e.g., [10][11][12]. In addition, fixed point methods also play an important role in solving various problems in data science, economics, medicine, and engineering; see, e.g., [6,[13][14][15][16][17] and the references therein. In order to find a fixed point of a nonlinear operator T : C → C, many researchers introduced various methods.…”

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

“…It is well-known that fixed point theory has relevant applications in many branches of analysis [1][2][3][4][5][6][7][8][9] and it can be applied to solving many areas of science and applied science, engineering, economics and medicine, such as image/signal processing [10][11][12][13][14][15][16][17] and modeling intensity modulated radiation theory treatment planning [18][19][20]. Many real life problems can be equivalently formulated as fixed point problems, meaning that one has to find a fixed point of some operators.…”