ABSTRACT
The purpose of this paper is to investigate the problem of finding a common element of the set of zero points of the sum of two operators and the fixed point set of a quasi-nonexpansive mapping. We introduce modified forward-backward splitting methods based on the so-called inertial forward-backward splitting algorithm, Mann algorithm and viscosity method. We establish weak and strong convergence theorems for iterative sequences generated by these methods. Our results extend and improve some related results in the literature.
Acknowledgments
The authors would like to thank the two referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Nguyen The Vinh http://orcid.org/0000-0003-3373-1881