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Теоремы о включении для многозначных отображений
Abstract
The paper is devoted to the investigation of some properties of multivalued mappings in Euclidean spaces. Fixed-point theorems are proved for multivalued mappings whose restrictions to a certain subset in the closure of a domain satisfy a “coacute angle condition” or a “strict coacute angle condition.” Similar results for the restrictions of multivalued mappings satisfying certain metric conditions are also obtained.
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We consider a mapping f(⋅) (in general nonlinear) from one topological linear space (TLS) X into another TLS Y. We investigate the problem of when a given element y∈Y is contained in the image of a set Ω⊂X under the mapping f(⋅).
The main results of the paper are various generalization (and their corollaries) of the well-known Brouwer theorem [1], one variant of which (see, [2] or [3]) is in turn, a multidimensional generalization of the Cauchy intermediate value theorem for continuous functions in R¹.
We obtain certain theorems on the solvability of equations as well as inclusions involving discontinuous and multivalued mappings (in the following, the generalizations are meant in this sense), which make it possible to investigate new classes of applied nonlinear boundary value problems.
Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convex norm is constructed. Here also an existence theorem and fixed-point theorem for general mappings are obtained. Moreover, certain remarks on the problem of existence of invariant subspaces of a linear continuous operator are given. Copyright (c) 2007 Kamal N. Soltanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We investigate the description of the image of a continuous mappings acting in a Banach space, and the solvability of equations and inclu-sions. The results obtained can be applied to the Cauchy problem for a nonlinear differential equation (or inclusion). In particular, a solvabil-ity theorem of the mixed problem for a nonlinear hyperbolic equation is proved, and one Nirenberg problem is studied.
Finite-Dimensional Linear Analysis. I. Linear Operators in Finite-Dimensional Vector Spaces (L)
- M A Muratov
- V L Ostrovskii
- Yu S Samoilenko
- MA Muratov
M. A. Muratov, V. L. Ostrovskii, and Yu. S. Samoilenko, Finite-Dimensional Linear Analysis. I. Linear Operators in Finite-Dimensional Vector Spaces (L) [in Russian], Tsentr Uchebn. Liter., Kiev (2011).
Fixed-point theorems for multivalued mappings
- Yu B Zelinskii
- B A Klishchuk
- M V Tkachuk