A cyclic iterative method for solving a class of variational inequalities in Hilbert spaces

ABSTRACT

The purpose of this paper is to introduce a new iterative method for solving a variational inequality over the set of common fixed points of a finite family of sequences of nearly non-expansive mappings in a real Hilbert space. And, using this result, we give some applications to the problem of finding a common fixed point of non-expansive mappings or non-expansive semigroups and the problem of finding a common null point of monotone operators.

KEYWORDS:

• Variational inequality
• sequence of nearly non-expansive mappings
• common fixed point
• common null point

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H06
• 47H09
• 47H10
• 47J25

Acknowledgements

The author would like to thank the referees and the editor for their valuable comments and suggestions which improved the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.