A modified extragradient method for variational inclusion and fixed point problems in Banach spaces

Abstract

In this work, we introduce a modified extragradient method for solving the fixed point problem of a nonexpansive mapping and the variational inclusion problem for two accretive operators in the framework of Banach spaces. We then prove its strong convergence under certain assumptions imposed on the parameters. As applications, we apply our main result to the variational inequality problem, split feasibility problem and the LASSO problem.

COMMUNICATED BY:

• B. Mordukhovich

Keywords:

• m-accretive operator
• Banach space
• strong convergence
• fixed point problem
• variational inclusion

2010 Mathematics Subject Classifications:

• 47H09
• 47H10
• 47J25
• 47J05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

P. Sunthrayuth was supported by RMUTT Research Grant for New Scholar under Grant NSF62D0602 and P. Cholamjiak was supported by the Thailand Research Fund and University of Phayao under Grant RSA6180084 and UOE 62001.