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Mat. Zametki, 2016, Volume 99, Issue 2, Pages 181–185 (Mi mz10711)  

This article is cited in 3 scientific papers (total in 3 papers)

On Surjective Quadratic Mappings

A. V. Arutyunov, S. E. Zhukovskii

Peoples Friendship University of Russia, Moscow

Abstract: In the paper, quadratic mappings acting from one finite-dimensional space to another are studied. Sufficient conditions for the stable surjectivity of a quadratic surjective mapping (i.e., for the condition that every quadratic mapping sufficiently close to a given one is also surjective) are obtained. The existence problem for nontrivial zeros of a surjective quadratic mapping acting from $\mathbb{R}^n$ to $\mathbb{R}^n$ is studied. For $n=3$, the absence of these zeros is proved.

Keywords: quadratic mapping, quadratic surjective mapping, stable surjectivity.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.333.2014/K
МК-5333.2015.1
Russian Foundation for Basic Research 15-01-04601


DOI: https://doi.org/10.4213/mzm10711

Full text: PDF file (419 kB)
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English version:
Mathematical Notes, 2016, 99:2, 192–195

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 05.11.2014
Revised: 18.09.2015

Citation: A. V. Arutyunov, S. E. Zhukovskii, “On Surjective Quadratic Mappings”, Mat. Zametki, 99:2 (2016), 181–185; Math. Notes, 99:2 (2016), 192–195

Citation in format AMSBIB
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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. V. Arutyunov, S. E. Zhukovskiy, “Properties of surjective real quadratic maps”, Sb. Math., 207:9 (2016), 1187–1214  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. V. Arutyunov, S. E. Zhukovskiy, D. Yu. Karamzin, “Some properties of two-dimensional surjective $p$-homogeneous maps”, Comput. Math. Math. Phys., 57:7 (2017), 1081–1089  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. Karzhemanov, I. Zhdanovskiy, “Some properties of surjective rational maps”, Eur. J. Math., 4:1 (2018), 326–329  crossref  mathscinet  zmath  isi  scopus
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