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Home » Issues » Archive of Issues » 2013 - 4 issue » pp. 36-54

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Russia Izhevsk
Year
2013
Issue
4
Pages
36-54
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Section Mathematics
Title The uniform approximation of recurrent functions and almost recurrent functions
Author(-s) Danilov L.I.a
Affiliations Physical Technical Institute, Ural Branch of the Russian Academy of Sciencesa
Abstract We consider the classes of functions $f:{\mathbb R}\to U,$ taking values in a metric space $(U,\rho ),$ which have Bochner transforms from the classes of recurrent functions and almost recurrent functions. We improve the preceding results on the uniform approximation of functions from classes under consideration by elementary functions from the same classes. These results can be applied to the investigation of the problem of the existence of almost recurrent selections for multivalued maps. The selections are supposed to satisfy a number of additional conditions. In the last section of the paper the variant of Lusin's theorem for recurrent functions is proved.
Keywords recurrent function, selection, multivalued mapping, Lusin's theorem
UDC 517.518.6
MSC 42A75, 54С65
DOI 10.20537/vm130405
Received 30 October 2013
Language Russian
Citation Danilov L.I. The uniform approximation of recurrent functions and almost recurrent functions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 36-54.
References
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