Book Review: Nonlinear mappings of monotone type
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 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 کاملDegree of mapping for nonlinear mappings of monotone type: Densely defined mapping.
The classical degree function constructed earlier for pseudomonotone mappings has been used to develop a broader degree theory of classical type for the sum of a maximal monotone map from a reflexive Banach space to its dual together with a bounded pseudomonotone map. The proof uses the generalized Yosida approximation of the maximal monotone mapping.
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 کاملOn an Operator Equation Involving Mappings of Monotone Type
Let X be a real reflexive Banach space and A: X — 2A a maximal monotone mapping such that the graph G(A) of A is weaklyclosed in X X X and 0 £/4(0). Also, let T: X — 2A be a quasi-bounded coercive mapping of type (M) such that the effective domain D(T) of T contains a dense linear subspace X of X. Then it is shown that for each * f I co e X there exists a u e X such that co e Au + Tu and the su...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1980
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1980-14732-1