A DSM proof of surjectivity of monotone nonlinear mappings
نویسندگان
چکیده
منابع مشابه
A DSM proof of surjectivity of monotone nonlinear mappings
Therefore, taking y = 0 without loss of generality, one concludes from (1) that f(x) ≤ 0 for x ≤ 0 and f(x) ≥ 0 for x ≥ 0. Since f is continuous, it follows that there is a point x0 such that f(x0) = 0. If y 6= 0 is an arbitrary real number, then the function F (x) = f(x) − y satisfies inequality (2) with F in place of f , provided that (2) holds for f . Condition (1) is also satisfied for F if...
متن کاملVariational Inequalities and Surjectivity for Set-valued Monotone Mappings
We denote by σ(F,E) the topology on F generated by the family {ω(x, ε) : x ∈ E, ε > 0} as a subbase for the neighbourhood system at 0. It is easy to show that, if F possesses the σ(F,E)-topology, F becomes a locally convex topological vector space. The σ(E,F )-topology on E is defined analogously. A subset X of E is said to be σ(E,F )-compact if X is compact related to the σ(E,F )-topology. Let...
متن کاملSurjectivity results for nonlinear mappings without oddness conditions
Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form λT (x)−S(x) = f , where T is invertible, and T, S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč́ık, Nečas, Souček, and Souček. We employ the concept of an a-stably-solvable operator, related to nonlinear spectral theory methodology. ...
متن کاملA System of Nonlinear Variational Inclusions with (A,)-Monotone Mappings
A new system of nonlinear variational inclusions involving A, η -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with A, η -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since A, η -monotonicity generalizes A-monotonicity and Hmonotonicity, our res...
متن کاملOn Nonlinear Variational Inclusions with (a, Η)-monotone Mappings
In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, η)-monotonicity generalizes A-monotoni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2009
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap95-2-4