Nonlinear maximal monotone operators in Banach space

Perturbations of Nonlinear Maximal Monotone Sets in Banach Space *

On the Eigenvalue Problem for Perturbed Nonlinear Maximal Monotone Operators in Reflexive Banach Spaces

Let X be a real reflexive Banach space with dual X∗ and G ⊂ X open and bounded and such that 0 ∈ G. Let T : X ⊃ D(T ) → 2X be maximal monotone with 0 ∈ D(T ) and 0 ∈ T (0), and C : X ⊃ D(C) → X∗ with 0 ∈ D(C) and C(0) = 0. A general and more unified eigenvalue theory is developed for the pair of operators (T,C). Further conditions are given for the existence of a pair (λ, x) ∈ (0,∞)× (D(T + C) ...

Existence and Perturbation Theorems for Nonlinear Maximal Monotone Operators in Banach Spaces by Felix E. Browder

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

Maximality of Sums of Two Maximal Monotone Operators in General Banach Space

We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural transversality conditions.

Strong Convergence of an Iterative Sequence for Maximal Monotone Operators in a Banach Space

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality probl...