On convexity of preimages of monotone operators. (English) Zbl 1196.47039
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.
The results proposed in this paper are new and extend, improve and unify the corresponding results in this field.
Reviewer: Hengyou Lan (Zigong)
MSC:
47H05 | Monotone operators and generalizations |
47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
49J40 | Variational inequalities |
90C31 | Sensitivity, stability, parametric optimization |
47E05 | General theory of ordinary differential operators |