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Alimov, Alexey Rostislavovich

Total publications: 64 (59)
in MathSciNet: 43 (41)
in zbMATH: 30 (28)
in Web of Science: 35 (34)
in Scopus: 36 (36)
Cited articles: 38
Citations in Math-Net.Ru: 281
Citations in MathSciNet: 151
Citations in Web of Science: 182
Citations in Scopus: 184
Presentations: 10

Number of views:
This page:5319
Abstract pages:12175
Full texts:4061
References:1234
Head Scientist Researcher
Doctor of physico-mathematical sciences (2015)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 31.08.1971
E-mail: ,
Keywords: best approximation, Chebyshev set, sun, strict sun.
UDC: 517.982.272, 517.982.256, 517.982, 517.982.252
MSC: 41A65, 41A65

Subject:

Theory of approximations in normed linear spaces.

   
Main publications:
  • A. R. Alimov, Sokhranenie approksimativnykh svoistv podmnozhestv chebyshevskikh mnozhestv i solnts v $\ell^\infty(n)$. Izv. RAN. Ser. matem., 2006, 70:5, 3–12.
  • A. R. Alimov, Monotonnaya lineinaya svyaznost chebyshevskikh mnozhestv v prostranstve $C(Q)$. Matem. sb., 2006, 197:9, 3–18.
  • A. R. Alimov, Geometricheskoe stroenie chebyshevskikh mnozhestv v $\ell^\infty(n)$. Funkts. analiz i ego pril., 2005, 39:1, 1–10.
  • A. R. Alimov, Svyaznost solnts v prostranstve $c_0$. Izv. RAN. Ser. matem., 2005, 69:4, 3–18.
  • A. R. Alimov, O strukture dopolneniya k chebyshevskim mnozhestvam. Funkts. analiz i ego pril., 2001, 35:3, 19–27.

http://www.mathnet.ru/eng/person13059
List of publications on Google Scholar
https://zbmath.org/authors/?q=ai:alimov.alexey-r
https://mathscinet.ams.org/mathscinet/MRAuthorID/602442
https://elibrary.ru/author_items.asp?authorid=14681
ISTINA http://istina.msu.ru/workers/3628613
http://orcid.org/0000-0001-8806-1593
http://www.researcherid.com/rid/M-3902-2015
https://www.scopus.com/authid/detail.url?authorId=7007117638
https://www.researchgate.net/profile/A_Alimov

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |



   2021
1. A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654  mathnet  crossref  crossref  mathscinet  isi  isi  elib  scopus
2. A. R. Alimov, I. G. Tsarkov, Spetskurs po klassicheskoi geometricheskoi teorii priblizhenii, OntoPrint, Moskva, 2021 , 210 pp.
3. A. R. Alimov, I. G. Tsar'kov, “Smoothness of subspace sections of the unit balls of $C(Q)$ and $L^1$”, J. Approx. Theory, 65 (2021), 105552 , 8 pp.  mathnet  crossref  isi  scopus;
4. A. R. Alimov, “Solarity of Chebyshev sets in dual spaces and uniquely remotal sets”, Lobachevskii J. Math., 42:4 (2021), 785–790  mathnet  crossref  mathscinet  isi  elib  scopus;
5. A. R. Alimov, I. G. Tsar'kov, “Approximatively Compact Sets in Asymmetric Efimov–Stechkin Spaces and Convexity of Almost Suns”, Math. Notes, 110:6 (2021), 947–951  mathnet  crossref  crossref  mathscinet  isi  scopus

   2020
6. A. R. Alimov, “Vypuklost i monotonnaya lineinaya svyaznost mnozhestv s nepreryvnoi metricheskoi proektsiei v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 26:2 (2020), 28-46  mathnet (cited: 3)  crossref  mathscinet  isi (cited: 4)  elib  scopus (cited: 3)
7. A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
8. A. R. Alimov, “Geometric construction of Chebyshev sets and suns in three-dimensional spaces with cylindrical norm”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 209–215  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
9. A. R. Alimov, A. A. Vasil'eva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 4, 70–71  mathnet
10. A. R. Alimov, A. A. Vasileva, S. V. Konyagin, A. S. Kochurov, A. I. Kozko, T. P. Lukashenko, K. S. Ryutin, V. M. Tikhomirov, A. V. Fursikov, V. N. Chubarikov, “Igor Germanovich Tsarkov (k shestidesyatiletiyu so dnya rozhdeniya)”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2020, no. 4, 70–71  mathnet

   2019
11. A. R. Alimov, “Continuity of the metric projection and local solar properties of sets”, Set-Valued Var. Anal., 27:1 (2019), 213–222  mathnet  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 4)
12. A. R. Alimov, E. V. Shchepin, “Suns are convex in tangent directions”, Dokl. Math., 99:1 (2019), 14–15  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
13. Alexey R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), 76 , 11 pp.  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
14. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 7)  elib  scopus (cited: 9)
15. A. R. Alimov, “Singularities of Solutions of the Eikonal Equation”, Differ. Equ., 55:10 (2019), 1311–1316  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus (cited: 1)
16. Alexey R. Alimov, Evgeny V. Shchepin, “Convexity of Suns in Tangent Directions”, J. Convex Anal., 26:4 (2019), 1071–1076  mathnet  mathscinet  zmath  isi (cited: 3)

   2018
17. A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 6)  elib  scopus (cited: 7)
18. A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)
19. A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast II. Priblizheniya klassami mnozhestv, dalneishee razvitie osnovnykh voprosov geometricheskoi teorii, OntoPrint, Moskva, 2018 , 350 pp.
20. A. R. Alimov, “Vyborki iz operatorov nailuchshego i pochti nailuchshego priblizheniya i solnechnost mnozhestv”, Sovremennye problemy matematiki i ee prilozhenii, Materialy mezhdunarodnoi nauchnoi konferentsii (Dushanbe, 21–22.06.2018), Filial Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, Tadzhikistan, 2018, 14–15
21. A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. of Institute of mathematics and mechanics, 44:1 (2018), 36–42  mathnet  mathscinet  zmath  scopus
22. Alexey R. Alimov, Evgeny E. Bukzhalev, “Iteration method of approximate solution of the Cauchy problem for a singularly perturbed weakly nonlinear differential equation of an arbitrary order”, Turk. J. Math., 42:5 (2018), 2841–2853  mathnet  crossref  mathscinet  zmath  isi  scopus
23. A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, Fundam. Prikl. Mat., 22:1 (2018), 3–11  mathnet  mathscinet
24. A. R. Alimov, “Lokalno chebyshevskie mnozhestva”, Vestnik Filiala Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, 2:1 (2018), 5-11  elib

   2017
25. A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 8)  elib  elib  scopus (cited: 8)
26. A. R. Alimov, “A monotone path-connected set with outer radially lower continuous metric projection is a strict sun”, Siberian Math. J., 58:1 (2017), 11–15  mathnet  crossref  crossref  isi (cited: 2)  elib  elib  scopus (cited: 2)
27. A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast I. Klassicheskie ponyatiya i konstruktsii priblizheniya mnozhestvami, OntoPrint, Moskva, 2017 , 346 pp.
28. A. R. Alimov, “O sootnoshenii mezhdu klassami solnts v nesimmetrichno normirovannykh prostranstvakh”, Trudy NIISI RAN, 7:1 (2017), 82–84  mathnet  mathscinet  elib
29. A. R. Alimov, I. G. Tsarkov, Osnovy geometricheskoi teorii priblizhenii. Chast II. Vypuklost i svyaznost chebyshevskikh mnozhestv i solnts, Obschestvo s ogranichennoi otvetstvennostyu “OntoPrint”, Moskva, 2017 , 130 pp.  elib

   2016
30. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 40)  elib  elib  scopus (cited: 33)
31. A. R. Alimov, “Mazur spaces and 4.3-intersection property of $(BM)$-spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:2 (2016), 133–137  mathnet  crossref  mathscinet  isi  elib
32. A. R. Alimov, “$P$-svyaznoe lokalno chebyshëvskoe mnozhestvo yavlyaetsya chebyshëvskim”, Trudy Mezhdunarodnoi letnei matematicheskoi Shkoly-Konferentsii S.B. Stechkina po teorii funktsii (g. Dushanbe, 15–25 avgusta 2016 g.), Poligrafiya OOO "Ofset Dushanbe, Dushanbe, 2016, 32–35  elib

   2015
33. A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18  mathnet (cited: 2)  isi (cited: 4)  elib
34. A. R. Alimov, “Svoistva peresecheniya sharov konechnomernykh (BM)-prostranstv”, Materialy mezhdunarodnoi konferentsii “Teoriya priblizhenii funktsii i rodstvennye zadachi analiza”, posvyaschennaya 100-letiyu so dnya rozhdeniya professora P. P. Korovkina, Teoriya priblizhenii funktsii i rodstvennye zadachi analiza (Kaluga, 09–10 oktyabrya 2015 g.), Izd-vo Kaluzhskogo gos. un-ta imeni K.E. Tsiolkovskogo, 2015, 17  elib
35. A. R. Alimov, E. Berdysheva, P. Butzer, W.zu Castell, W. Dahmen, R. DeVore, F. Filibr, K. Jetter, H. Mhaskar, P. Nevai, T. Sauer, L. Schumaker, M. Sommer, H. Strauss, Hu Yu, “Hubert A. Berens (1936–2015)”, J. Approx. Theory, 198 (2015), iv–xxix  crossref  mathscinet  zmath

   2014
36. A. R. Alimov, “The Rainwater–Simons weak convergence theorem for the Brown associated norm”, Eurasian Math. J., 5:2 (2014), 126–131  mathnet (cited: 2)  elib (cited: 1)

   2016
37. A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730  mathnet  crossref  mathscinet  elib  elib

   2014
38. A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 15)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 14)
39. A. R. Alimov, “Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 489–497  mathnet  crossref  elib

   2012
40. A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in spaces with linear ball embedding”, Eurasian Math. J., 3:2 (2012), 21–30  mathnet (cited: 4)  mathscinet  zmath

   2014
41. A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454  mathnet  crossref  elib (cited: 2)  scopus (cited: 6)

   2013
42. A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, J. Math. Sci., 191:5 (2013), 599–604  mathnet  crossref  elib (cited: 1)  scopus (cited: 2)

   2012
43. A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in the space $C(Q)$”, J. Math. Sci., 185:3 (2012), 360–366  mathnet  crossref  elib  scopus
44. A. R. Alimov, “A Monotone Path Connected Chebyshev Set Is a Sun”, Math. Notes, 91:2 (2012), 290–292  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 5)
45. A. R. Alimov, “Ogranichennaya strogaya solnechnost strogikh solnts v prostranstve $C(Q)$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 6, 16–19  mathnet (cited: 3); A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$”, Moscow University Mathematics Bulletin, Moscow University Mechanics Bulletin, 68:1 (2013), 14–17  crossref  scopus (cited: 1)

   2008
46. A. R. Alimov, “Sokhranenie approksimativnykh svoistv chebyshëvskikh mnozhestv i solnts na ploskosti”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 63:4 (2008), 46–49  mathnet (cited: 6)  crossref  mathscinet  zmath  elib  scopus (cited: 5)

   2006
47. A. R. Alimov, “Preservation of approximative properties of subsets of Chebyshev sets and suns in $\ell^\infty (n)$”, Izv. Math., 70:5 (2006), 857–866  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 5)
48. A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$”, Sb. Math., 197:9 (2006), 1259–1272  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 17)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 18)

   2005
49. A. R. Alimov, “The Geometric Structure of Chebyshev Sets in $\ell^\infty(n)$”, Funct. Anal. Appl., 39:1 (2005), 1–8  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 8)  scopus (cited: 11)
50. A. R. Alimov, “Connectedness of suns in the space $c_0$”, Izv. Math., 69:4 (2005), 651–666  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)
51. A. R. Alimov, “Convexity of Chebyshev Sets Contained in a Subspace”, Math. Notes, 78:1 (2005), 3–13  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)
52. A. R. Alimov, “Geometric construction of Chebyshev sets in the spaces $\ell^\infty(n)$, $c_0$ and $c$”, Russian Math. Surveys, 60:3 (2005), 559–561  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  elib  scopus (cited: 1)

   2004
53. A. R. Alimov, “Characterisations of Chebyshev sets in $c_0$”, J. Approx. Theory, 129:2 (2004), 217–229  crossref  mathscinet  zmath  elib  scopus (cited: 8)

   2003
54. A. R. Alimov, “The Banach–Mazur theorem for spaces with an asymmetric distance”, Russian Math. Surveys, 58:2 (2003), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  scopus (cited: 4)

   2001
55. A. R. Alimov, “On the Structure of the Complements of Chebyshev Sets”, Funct. Anal. Appl., 35:3 (2001), 176–182  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 19)  elib (cited: 5)  scopus (cited: 20)
56. A. R. Alimov, “Geometrical Characterization of Strict Suns in $\ell^\infty(n)$”, Math. Notes, 70:1 (2001), 3–10  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 9)  elib
57. A. R. Alimov, M. I. Karlov, “Sets with External Chebyshev Layer”, Math. Notes, 69:2 (2001), 269–273  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib

   1999
58. A. R Alimov, H. Berens, “Examples of Chebyshev sets in matrix spaces”, J. Approx. Theory, 99:1 (1999), 44–53  crossref  mathscinet  zmath  elib  scopus (cited: 2)

   1998
59. A. R. Alimov, “Solstice property for a system of 2-spaces”, East J. Approx., 4:1 (1998), 25–34  mathscinet  zmath
60. A. R. Alimov, Mat. Pros., 2, MCCME, Moscow, 1998, 155–172  mathnet

   1997
61. A. R. Alimov, “Chebyshev Compact Sets in the Plane”, Proc. Steklov Inst. Math., 219 (1997), 2–19  mathnet  mathscinet  zmath

   1996
62. A. R. Alimov, “Chebyshev set's complement”, East J. Approx., 2:2 (1996), 215–232  mathscinet  zmath

   1995
63. A. R. Alimov, “A number of connected components of sun's complement”, East J. Approx., 1:4 (1995), 419–429  mathscinet  zmath
64. A. R. Alimov, “Letter to the editor”, Math. Notes, 58:3 (1995), 1010  mathnet  crossref  mathscinet  zmath  isi

Presentations in Math-Net.Ru
1. Some solar problems in $\max$- and $\min$-approximation
A. R. Alimov
International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin
September 9, 2021 15:30   
2. Chebyshev sets and suns in a finite-dimensional space
A. R. Alimov
Optimization and nonlinear analysis
February 4, 2021 14:00   
3. Выпуклость чебышёвских множеств и солнц по касательным направлениям
A. R. Alimov
Knots and Representation Theory
March 11, 2019
4. Решение задач о гладких C^1-решений уравнения эйконала, принцип отражения, зеркала
I. G. Tsar'kov, A. R. Alimov
Geometric Theory of Optimal Control
March 14, 2018 18:30
5. Локальные и глобальные аппроксимативно-геометрические свойства множеств
A. R. Alimov
Seminar on Approximation Theory
November 16, 2017 10:30
6. Selections from the best and near-best approximation operator
A. R. Alimov
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 2, 2017 16:05
7. Непрерывность метрической проекции, выборки из нее и солнечные свойства множеств
A. R. Alimov

March 21, 2017 17:30
8. Солнечные свойства множеств непрерывной метрической проекции
A. R. Alimov
Seminar on Approximation Theory
April 14, 2016 10:30
9. Связность строгих солнц в конечномерных банаховых пространствах
A. R. Alimov
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 25, 2015 14:30
10. Свзяность солнц и чебышёвских множеств в задачах наилучшего приближения
A. R. Alimov
Seminar on Approximation Theory
February 20, 2014 10:30

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