A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds

Abstract

In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g-pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.

Keywords:

• Mixed weak vector variational inequality
• gap function
• generalized monotone
• KKM mapping
• Hadamard manifold

Mathematics subject classifications (2010):

• 58E35
• 47H05

Acknowledgments

The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II.