Geodesic
On topological properties of the set of solutions of operator inclusions with a multi-valued Lipschitz right-hand side
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 11-15

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This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form $A(x)\in\lambda F(x)$, where $A$ is a bounded linear surjective operator, and $F$ is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator $A$ and the dimension of the set of solutions of this inclusion.
Keywords: multivalued mapping, Hausdorff metric, contractive mapping, surjective operator. 
@article{IVM_2021_5_a2,
     author = {B. D. Gel'man},
     title = {On topological properties of the set of solutions of operator inclusions with a multi-valued {Lipschitz} right-hand side},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--15},
     publisher = {mathdoc},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_5_a2/}
}
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B. D. Gel'man. On topological properties of the set of solutions of operator inclusions with a multi-valued Lipschitz right-hand side. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 11-15. http://geodesic.mathdoc.fr/item/IVM_2021_5_a2/