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Mat. Zametki, 2005, Volume 78, Issue 2, Pages 212–222 (Mi mz2649)  

This article is cited in 4 scientific papers (total in 4 papers)

Continuous Approximations of Multivalued Mappings and Fixed Points

B. D. Gel'man

Voronezh State University

Abstract: In the present paper, we prove a fixed-point theorem for completely continuous multivalued mappings defined on a bounded convex closed subset $X$ of the Hilbert space $H$ which satisfies the tangential condition $F(x)\cap(x+T_X(x))\ne\varnothing$, where $T_X(x)$ is the cone tangent to the set $X$ at a point $x$. The proof of this theorem is based on the method of single-valued approximations to multivalued mappings. In this paper, we consider a simple approach for constructing single-valued approximations to multivalued mappings. This approach allows us not only to simplify the proofs of already-known theorems, but also to obtain new statements needed to prove the main theorem in this paper.

DOI: https://doi.org/10.4213/mzm2649

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English version:
Mathematical Notes, 2005, 78:2, 194–203

Bibliographic databases:

UDC: 517.986.6
Received: 29.10.2002
Revised: 25.10.2004

Citation: B. D. Gel'man, “Continuous Approximations of Multivalued Mappings and Fixed Points”, Mat. Zametki, 78:2 (2005), 212–222; Math. Notes, 78:2 (2005), 194–203

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. D. Gel'man, “On the Cauchy Problem for a Class of Degenerate Differential Equations with Lipschitz Right-Hand Side”, Funct. Anal. Appl., 42:3 (2008), 227–229  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Arutyunov A., Gelman B., Obukhovskii V., “a Coincidence Theorem For Multivalued Maps and Its Applications”, J. Fixed Point Theory Appl., 17:2 (2015), 331–340  crossref  mathscinet  zmath  isi  scopus  scopus
    3. B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. B. D. Gel'man, “A Hybrid Fixed-Point Theorem for Set-Valued Maps”, Math. Notes, 101:6 (2017), 951–959  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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