Implicit eigenvalue problems for maximal monotone operators
نویسندگان
چکیده
منابع مشابه
Implicit eigenvalue problems for maximal monotone operators
where T is a maximal monotone multi-valued operator and the operator C satisfies condition (S+) or (S̃+). In a regularization method by the duality operator, we use the degree theories of Kartsatos and Skrypnik upon conditions of C as well as Browder’s degree. There are two cases to consider: One is that C is demicontinuous and bounded with condition (S+); and the other is that C is quasibounded...
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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) ...
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It is shown that a set-valued map M : R ⇒ R is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replace...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2012
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2012-178