Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

Abstract

In this article, we introduce and consider a general system of variational inequalities. Using the projection technique, we suggest and analyse new iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results improve and extend the recent ones announced by many others.

Keywords:

• variational inequality
• projection method
• relaxed cocoercive mapping
• Hilbert space

AMS Subject Classifications::

• 47H04
• 47H06
• 47J25
• 49J40
• 65B05

Acknowledgements

The authors are extremely grateful to the referees for useful suggestions that improved the content of the article.