A class of generalized monotone operators

We consider the class of η-monotone operators which is intermediate between the class of Minty–Browder and the class of h-monotone operators. We provide sufficient conditions for η-monotonicity which generates a class of η-monotone operators. As a result we construct several η-monotone operators which fill the lack of examples in [11] of h-monotone operators. By using one of the main results in [11], applied to η-monotone operators, we prove a global injectivity theorem. Despite the infinite dimensional contexts in which the Minty–Browder monotonicity is generally used, the motivation behind the present work is rather geometric and the results proved here concern mostly the finite dimensional context.