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.
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