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Russia Tambov
Section  Mathematics 
Title  On fixed points of multivalued maps in metric spaces and differential inclusions 
Author(s)  Zhukovskiy E.S.^{a}, Panasenko E.A.^{a} 
Affiliations  Tambov State University^{a} 
Abstract  A generalization of the Nadler fixed point theorem for multivalued maps acting in metric spaces is proposed. The obtained result allows to study the existence of fixed points for multivalued maps that have as images any arbitrary sets of the corresponding metric space and are not necessarily contracting, or even continuous, with respect to the Hausdorff metric. The mentioned result can be used for investigating differential and functionaldifferential equations with discontinuities and inclusions generated by multivalued maps with arbitrary images. In the second part of the paper, as an application, conditions of existence and continuation of solutions to the Cauchy problem for a differential inclusion with noncompact in $\mathbb{R}^n$ righthand side are derived. 
Keywords  multivalued map, fixed point, differential inclusion 
UDC  515.126.83, 515.126.4, 517.911.5 
MSC  47H04, 47H10, 34A60 
DOI  10.20537/vm130202 
Received  1 February 2013 
Language  English 
Citation  Zhukovskiy E.S., Panasenko E.A. On fixed points of multivalued maps in metric spaces and differential inclusions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 2, pp. 1226. 
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