Fixed point methods for pseudomonotone variational inequalities involving strict pseudocontractions

Abstract

We introduce a new iteration method for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of strict pseudocontractions in a real Hilbert space. The weak convergence of the iterative sequences generated by the method is obtained thanks to improve and extend some recent results under the assumptions that the cost mapping associated with the variational inequality problem only is pseudomonotone and not necessarily inverse strongly monotone. Finally, we present some numerical examples to illustrate the behaviour of the proposed algorithm.

Keywords:

• variational inequality problem
• pseudomonotone
• linesearch
• projection method
• strict pseudocontractions

AMS Subject Classifications:

• 2010
• 65 K10
• 90 C25

Acknowledgments

We are very grateful to two anonymous referees for their really helpful and constructive comments in improving the paper.

Notes

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under [grant number 101.02-2013.03].