Inertial methods for fixed point problems and zero point problems of the sum of two monotone mappings

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.

KEYWORDS:

• Mann algorithm
• viscosity method
• inertial method
• forward-backward splitting method
• fixed point problem

AMS CLASSIFICATIONS:

• 65Y05
• 65K15
• 68W10
• 47H05
• 47H10

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

Additional information

Funding

The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No.101.01-2017.08.