Unique solvability of weakly homogeneous generalized variational inequalities

An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which one the key conditions to ensure unique solvability generalized variational inequality. This paper focuses on studying uniqueness and inequality with a pair mappings. By using weaker condition than strong monotonicity some additional conditions, we achieve several results underlying problem, are exported by making use exceptional family elements. As an adjunct, also obtain nonemptiness compactness solution sets under appropriate conditions. The conclusions presented in this new or supplements existing ones even when problem comes down its important subclasses studied recent years.