A theorem of variational inclusion problems and various nonlinear mappings

ABSTRACT

In this paper, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of a finite family of variational inclusion problems in Hilbert spaces. Moreover, we utilize our main result to fixed point problems of various nonlinear mappings and the set of solutions of variational inclusion problems.

KEYWORDS:

• Variational inclusion problems
• nonexpansive mapping
• resolvent operator
• fixed point problem

AMS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Research Administration Division of King Mongkut’s Institute of Technology Ladkrabang.