Abstract
In this study, we extend the weighted variational inequality problem (WVIP) and the Minty weighted variational inequality problem (MWVIP) from linear spaces to nonlinear spaces, specifically Hadamard manifolds, and show the relationships between WVIP and vector variational inequalities. In addition, we establish the concept of weighted monotonicities on the Hadamard manifold and prove the existence of many solutions.
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