A projection-type method for solving multi-valued variational inequalities and fixed point problems

Abstract

In this paper, we introduce a projection algorithm for finding a common element of the set Fix(T) of fixed points of a -strict pseudocontraction mapping and the set S of solutions of a multi-valued variational inequality problem without monotonicity. We show that the sequence generated by our method is globally convergent to some common element of Fix(T) and S, provided that the mapping F is continuous with nonempty compact convex values. Preliminary numerical experiments are reported.

Keywords:

• Projection-type method
• multi-valued variational inequality
• -strict pseudocontraction
• fixed point problem

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 11771350]; Basic and Advanced Research Project of CQ CSTC [grant number cstc2016jcyjA0163]; Science and Technology Project of Chongqing Municipal Education Committee of China [grant number KJ1600433]; Chongqing Research and Innovation Project of Graduate Students [number CYS16173].