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Mat. Zametki, 2005, Volume 77, Issue 4, Pages 483–497 (Mi mz2507)  

This article is cited in 15 scientific papers (total in 15 papers)

Covering of nonlinear maps on a cone in neighborhoods of irregular points

A. V. Arutyunov

Peoples Friendship University of Russia

Abstract: Inverse function theorems for smooth nonlinear maps defined on convex cones in Banach spaces in a neighborhood of an irregular point are considered. The corresponding covering theorem is proved. The proofs are based on a Banach open mapping theorem for convex cones in Banach spaces, which is also proved in the paper. Sufficient conditions for tangency to the zero set of a nonlinear map without a priori regularity assumptions are obtained.

DOI: https://doi.org/10.4213/mzm2507

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English version:
Mathematical Notes, 2005, 77:4, 447–460

Bibliographic databases:

UDC: 518.9
Received: 01.03.2004

Citation: A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Mat. Zametki, 77:4 (2005), 483–497; Math. Notes, 77:4 (2005), 447–460

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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. A. V. Arutyunov, “Implicit-Function Theorem on the Cone in a Neighborhood of an Irregular Point”, Math. Notes, 78:4 (2005), 573–576  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Arutyunov, AV, “Sensitivity analysis for cone-constrained optimization problems under the relaxed constraint qualifications”, Mathematics of Operations Research, 30:2 (2005), 333  crossref  mathscinet  zmath  isi  scopus
    3. Arutyunov A. K., Izmailov A. F., “Directional stability theorem and directional metric regularity”, Math. Oper. Res., 31:3 (2006), 526–543  crossref  mathscinet  zmath  isi  elib  scopus
    4. Avakov E. R., Arutyunov A. V., Izmailov A. F., “Necessary conditions for an extremum in 2-regular problems”, Dokl. Math., 73:3 (2006), 340–343  crossref  mathscinet  zmath  isi  elib  scopus
    5. D. Yu. Karamzin, “On necessary extremum conditions for finite-dimensional problems with inequality constraints”, Comput. Math. Math. Phys., 46:11 (2006), 1860–1871  mathnet  crossref  mathscinet
    6. A. V. Arutyunov, “An implicit function theorem without a priori assumptions about normality”, Comput. Math. Math. Phys., 46:2 (2006), 195–205  mathnet  crossref  mathscinet  zmath  elib  elib
    7. E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Proc. Steklov Inst. Math., 256 (2007), 2–25  mathnet  crossref  mathscinet  zmath  elib  elib
    8. Arutyunov A. V., Avakov E. R., Izmailov A. F., “Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications”, Math. Program., 114:1, Ser. A (2008), 37–68  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. V. Arutyunov, “On implicit function theorems at abnormal points”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S18–S27  mathnet  crossref  isi  elib
    10. Arutyunov A.V., Zhukovskiy S.E., “Existence of local solutions in constrained dynamic systems”, Appl Anal, 90:6 (2011), 889–898  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Uderzo A., “On Mappings Covering at a Nonlinear Rate and their Perturbation Stability”, Nonlinear Anal.-Theory Methods Appl., 75:3 (2012), 1602–1616  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Zhukovskii S.E., Mingaleeva Z.T., “Suschestvovanie i nepreryvnost neyavnoi funktsii v okrestnosti anormalnoi tochki”, Vestnik moskovskogo universiteta. seriya 15: vychislitelnaya matematika i kibernetika, 2 (2012), 10–15  mathscinet  elib
    14. Huynh Van Ngai, Thera M., “Directional Metric Regularity of Multifunctions”, Math. Oper. Res., 40:4 (2015), 969–991  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Arutyunov A.V., Izmailov A.F., “Stability of Possibly Nonisolated Solutions of Constrained Equations, With Applications to Complementarity and Equilibrium Problems”, Set-Valued Var. Anal., 26:2 (2018), 327–352  crossref  mathscinet  zmath  isi  scopus  scopus
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