The purpose of this paper is to study the relationship between local and global Minty-Browder monotone operators and then to show that these operators have generally convex preimages. The results presented in this paper allow to show that positive semidefiniteness on the complement of a discrete set of a differential operator implies the Minty-Browder monotonicity of the operator itself. Furthermore, some injectivity/univalency theorems that generalize some well-known results are obtained.
The results proposed in this paper are new and extend, improve and unify the corresponding results in this field.