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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 2(6), Pages 292–300 (Mi msb1742)  

This article is cited in 8 scientific papers (total in 8 papers)

On the question of the existence of continuous branches of multivalued mappings with nonconvex images in spaces of summable functions

A. I. Bulgakov


Abstract: Let $B$ be a Banach space with norm $\|\cdot\|$, and let $(E,\mathfrak M)$ be a compact topological space with $\sigma$-algebra of measurable sets $\mathfrak M$ on which a nonnegative regular Borel measure $\mu$ is given. Further, let $L_1(E,B)$ be the Banach space of Bochner-integrable functions $u\colon E\to B$, with the norm $\|u\|_{L_1(E,B)}=\int_E\|u(t)\| d\mu$, and let $\Phi\colon K\to2^{L_1(E,B)}$ be a multivalued mapping and $P\colon K\to L_1(E,B)$ a single-valued mapping, where $K$ is a compact topological space. Under certain assumptions it is proved that for any $\varepsilon>0$ there exists a continuous mapping $g\colon K\to L_1(E,B)$ such that the following conditions hold for any $x\in K$: $g(x)\in\Phi(x)$, and $\|P(x)-g(x)\|_{L_1(E,B)}<\rho_{L_1(E,B)}[P(x),\Phi(x)]+\varepsilon$, where $\rho_{L_1(E,B)}[ \cdot {,} \cdot ]$ is the distance in $L_1(E,B)$ from a point to a set.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 295–303

Bibliographic databases:

UDC: 517.965
MSC: Primary 54C65; Secondary 46E30
Received: 13.01.1987

Citation: A. I. Bulgakov, “On the question of the existence of continuous branches of multivalued mappings with nonconvex images in spaces of summable functions”, Mat. Sb. (N.S.), 136(178):2(6) (1988), 292–300; Math. USSR-Sb., 64:1 (1989), 295–303

Citation in format AMSBIB
\Bibitem{Bul88}
\by A.~I.~Bulgakov
\paper On the question of the existence of continuous branches of multivalued mappings with nonconvex images in spaces of summable functions
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 2(6)
\pages 292--300
\mathnet{http://mi.mathnet.ru/msb1742}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=954930}
\zmath{https://zbmath.org/?q=an:0711.46025|0664.46025}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 295--303
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003308}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Bulgakov, “Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side”, Math. USSR-Sb., 71:2 (1992), 273–287  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Bulgakov A., “Averaging of Functional-Differential Inclusions”, Differ. Equ., 26:10 (1990), 1236–1245  mathnet  mathscinet  zmath  isi
    3. Goncharov V., Tolstonogov A., “On Continuous Selectors and Properties of Solutions of Differential-Inclusions with M-Accretive Operators”, 315, no. 5, 1990, 1035–1039  mathscinet  zmath  isi
    4. V. V. Goncharov, A. A. Tolstonogov, “Joint continuous selections of multivalued mappings with nonconvex values, and their applications”, Math. USSR-Sb., 73:2 (1992), 319–339  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Bulgakov A., “Continuous-Selections of Multivalued Mappings and Integral Inclusions with Nonconvex Values and their Applications .1.”, Differ. Equ., 28:3 (1992), 303–311  mathnet  mathscinet  zmath  isi
    6. A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko, “On the theory of perturbed inclusions and its applications”, Sb. Math., 196:10 (2005), 1421–1472  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. A. I. Bulgakov, A. I. Korobko, “K voprosu o suschestvovanii obobschennogo resheniya vozmuschennogo vklyucheniya”, Izv. IMI UdGU, 2006, no. 2(36), 9–12  mathnet
    8. L. I. Danilov, “Shift dynamical systems and measurable selectors of multivalued maps”, Sb. Math., 209:11 (2018), 1611–1643  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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