Strong convergence of a self-adaptive method for the split feasibility problem

Abstract

Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e.g., variational inequality problems. We devote this paper to developing and improving the self-adaptive methods for solving the split feasibility problem. A new improved self-adaptive method is introduced for solving the split feasibility problem. As a special case, the minimum norm solution of the split feasibility problem can be approached iteratively. MSC:47J25, 47J20, 49N45, 65J15.

Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

“…It has been found that the SFP (1.1) can be used in many areas such as image restoration, computer tomograph, and radiation therapy treatment planning. Some methods have been proposed to solve split feasibility problems; see, for instance, [1,17,18,19]. Note that if the SFP (1.1) is consistent, it is no hard to see that x * solves the SFP (1.1) if and only if it solves the fixed point equation x * = P C (I − γA * (I − P Q )A)x * ,…”

A projected fixed point algorithm with Meir-Keeler contraction for pseudocontractive mappings

“…In the literature, there are a large number references associated with the fixed point algorithms for nonexpansive mappings and pseudocontractive mappings. See, for instance, [1][2][3][4][5][6][7]11] and [9,10,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The first interesting result for finding the fixed points of the pseudocontractive mappings was presented by Ishikawa in 1974 as follows.…”

Hybrid shrinking iterative solutions to convex feasibility problems and a system of generalized mixed equilibrium problems

“…In addition, the concept of cycle of the sequence of mappings was presented in this paper. The results of this article modify and improve the results of Deng and Qian [21], it also in some sense, improves some results of [23][24][25][26][27]29]. …”