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.
Bibliographical noteFunding Information:
This work is financially supported by the Council of Scientific and Industrial Research, New Delhi, India through Grant No.: 25(0266)/17/EMR-II. The authors are thankful to referees for their valuable remarks which improved the results and presentation of this article.
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- Hadamard manifold
- KKM mapping
- Mixed weak vector variational inequality
- gap function
- generalized monotone
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics