Self-Adaptive Method and Inertial Modification for Solving the Split Feasibility Problem and Fixed-Point Problem of Quasi-Nonexpansive Mapping

Yuanheng Wang, Tiantian Xu, Jen-Chih Yao and Bingnan Jiang
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Yuanheng Wang: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Tiantian Xu: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Jen-Chih Yao: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
Bingnan Jiang: College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2022, vol. 10, issue 9, 1-15

Abstract: The split feasibility problem (SFP) has many practical applications, which has attracted the attention of many authors. In this paper, we propose a different method to solve the SFP and the fixed-point problem involving quasi-nonexpansive mappings. We relax the conditions of the operator as well as consider the inertial iteration and the adaptive step size. For example, the convergence generated by our new method is better than that of other algorithms, and the convergence rate of our algorithm greatly improves that of previous algorithms.

Keywords: iterative method; inertial method; quasi-nonexpansive mapping; fixed point; split feasibility problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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