Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings

• Main Authors: Tongxin Xu, Luoyi Shi
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Journal of Inequalities and Applications
• Subjects: Mutiple-sets split feasibility problem; Split equality fixed point problem; Strong convergence; Hilbert spaces; Iterative algorithm
• Online Access: https://doi.org/10.1186/s13660-021-02656-1

Abstract In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.