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Alimov Alexey Rostislavovich
(recent publications)

by years

scientific publications

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1.	A. R. Alimov, I. G. Tsar'kov, “Approximative properties of sets relative to their metric exterior”, Izv. RAN. Ser. Mat. (to appear)

2026
2.	A. R. Alimov, I. G. Tsar'kov, “Approximative weak compactness”, Sb. Math., 217:3 (2026), 295–314
3.	A. R. Alimov, N. A. Ilyasov, “Individualnye approksimativnye svoistva mnozhestv i approksimativnaya kompaktnost”, Matematicheskie trudy, 29:1 (2026), 5-17
4.	N. A. Ilyasov, A. R. Alimov, “On an extremal Gheit function and its applications”, Russ. J. Math. Phys., 33:1 (2026), 1-11
5.	A. R. Alimov, I. G. Tsar'kov, “Approximative properties of multivariate exponential sums”, Russ. J. Math. Phys., 33:1 (2026), 12–23
6.	A. R. Alimov, N. A. Ilyasov, “Points of Monotone Connectedness and Solar Properties of Sets”, Russ. J. Math. Phys, 33:2 (2026), 195-201

2025
7.	A. R Alimov, “Hereditary properties of lower semicontinuous metric projection and solar properties of sets”, J. Anal., 33:2 (2025), 743–753	2 ^[x]
8.	A. R. Alimov, I. G. Tsar'kov, “Stability of approximation in classical problems of geometric approximation theory”, Izv. Math., 89:6 (2025), 1087–1107
9.	A.R.Alimov,, N.A. Ilyasov, “Approximative compactness and acting points”, Russ. J. Math. Phys., 32:2 (2025), 219-227	5 ^[x]
10.	A. R. Alimov, I. G. Tsar'kov, “Projection Closed Sets and Efimov–Stechkin Spaces”, Proc. Steklov Inst. Math., 331: suppl. 1 (2025), S1–S13
11.	A. R. Alimov, N. A. Ilyasov, “Convexity of out-Chebyshev sets”, Baku Math.J., 4:2 (2025), 231-236
12.	A. R. Alimov, I. G. Tsarkov, Sovremennye voprosy geometricheskoi teorii priblizhenii, Izdatelskii dom MGU, Moskva, 2025
13.	A. R. Alimov, “Suschestvovanie drobno-ratsionalnogo priblizheniya v nesimmetrichnykh prostranstvakh”, Fund. Prikl. Matem., 25:4 (2025), 29-35

2024
14.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
15.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev unions of planes, and their approximative and geometric properties”, J. Approx. Theory, 298 (2024), 106009, 12 pp.	12 ^[x]
16.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of subspaces in asymmetric normed spaces”, Izv. Math., 88:6 (2024), 1032–1049
17.	A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
18.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259	12 ^[x]
19.	A. R. Alimov, I. G. Tsarkov, “Monotonno lineino svyaznye mnozhestva v geometricheskoi teorii priblizheniya i ee prilozheniyakh”, Matematika i teoreticheskie kompyuternye nauki, 2:2 (2024), 30-46
20.	A. R. Alimov, “Balayage theorems for connectedness problems in uniformly convex spaces”, Proc. Institute Math. Mech., 50:1 (2024), 53–61
21.	A. R. Alimov, “Strict suns composed of planes”, Proc. Steklov Inst. Math. (Suppl.), 327, suppl. 1 (2024), S1–S9

2023
22.	A. R. Alimov, I. G. Tsarkov, Sovremennaya geometricheskaya teoriya priblizhenii, “OntoPrint”, Moskva, 2023, 425 pp.
23.	A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31 (2023), 2287–2295	3 ^[x]
24.	A. R. Alimov, “Strict Protosuns in Asymmetric Spaces of Continuous Functions”, Results in Mathematics, 78 (2023), 95, 15 pp.	13 ^[x]
25.	A. R. Alimov, I. G. Tsar'kov, “Max-solar properties of sets in normed and asymmetrically normed spaces”, J. Convex Analysis, 30:1 (2023), 159–174
26.	A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
27.	A. R. Alimov, “Universality theorems for asymmetric spaces”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 26:2 (2023), 2250017, 11 pp.	6 ^[x]
28.	A. R Alimov, “Approximative solar properties of sets and local geometry of the unit sphere”, Lobachevskii Journal of Mathematics, 44:12 (2023), 5142–5148	6 ^[x]

2022
29.	Alexey R. Alimov, Igor' G. Tsarkov, Geometric Approximation Theory, Springer Monographs in Mathematics, Springer, 2022, xxi+508 pp.	57 ^[x]
30.	A. R Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii Journal of Mathematics, 43:3 (2022), 519–-527	10 ^[x]
31.	Alexey R. Alimov, Igor' G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Result. Math., 77 (2022), 86	23 ^[x]
32.	A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
33.	A. R. Alimov, “Tomographic characterizations of suns in three-dimensional spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 2, 2022, 45–55
34.	Alexey R. Alimov, Igor' G. Tsar'kov, “Suns, moons, and $\mathring B$-complete sets in asymmetric spaces”, Set-Valued Var. Anal., 30 (2022), 1233–1245	26 ^[x]
35.	A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
36.	A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
37.	A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces C(Q) and Lp”, Russian Journal of Mathematical Physics, 29:3 (2022), 291-305	17 ^[x]

2021
38.	A. R. Alimov, B. B. Bednov, “Monotone path-connectedness of Chebyshev sets in three-dimensional spaces”, Sb. Math., 212:5 (2021), 636–654
39.	A. R. Alimov, I. G. Tsarkov, Spetskurs po klassicheskoi geometricheskoi teorii priblizhenii, OntoPrint, Moskva, 2021, 210 pp.
40.	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.	10 ^[x]
41.	A. R. Alimov, “Solarity of Chebyshev sets in dual spaces and uniquely remotal sets”, Lobachevskii J. Math., 42:4 (2021), 785–790	3 ^[x]
42.	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

2020
43.	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	8 ^[x]
44.	A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Math. Notes, 108:3 (2020), 309–317
45.	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
46.	A. R. Alimov, “Geometricheskoe stroenie chebyshevskikh mnozhestv i solnts v trekhmernykh prostranstvakh s tsilindricheskoi normoi”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2020, no. 5, 26–32	1 ^[x]

2019
47.	A. R. Alimov, “Continuity of the metric projection and local solar properties of sets”, Set-Valued Var. Anal., 27:1 (2019), 213–222	6 ^[x]
48.	A. R. Alimov, E. V. Shchepin, “Suns are convex in tangent directions”, Dokl. Math., 99:1 (2019), 14–15
49.	Alexey R. Alimov, “Solarity of sets in max-approximation problems”, J. Fixed Point Theory Appl., 21:3 (2019), 76, 11 pp.	5 ^[x]
50.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
51.	A. R. Alimov, “Singularities of Solutions of the Eikonal Equation”, Differ. Equ., 55:10 (2019), 1311–1316
52.	Alexey R. Alimov, Evgeny V. Shchepin, “Convexity of Suns in Tangent Directions”, J. Convex Anal., 26:4 (2019), 1071–1076

2018
53.	A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368
54.	A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
55.	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.
56.	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
57.	A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. of Institute of mathematics and mechanics, 44:1 (2018), 36–42
58.	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

2020
59.	A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, J. Math. Sci., 250:3 (2020), 385–390

2018
60.	A. R. Alimov, “Lokalno chebyshevskie mnozhestva”, Vestnik Filiala Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, 2:1 (2018), 5-11

2017
61.	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
62.	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
63.	A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast I. Klassicheskie ponyatiya i konstruktsii priblizheniya mnozhestvami, OntoPrint, Moskva, 2017, 346 pp.
64.	A. R. Alimov, “O sootnoshenii mezhdu klassami solnts v nesimmetrichno normirovannykh prostranstvakh”, Trudy NIISI RAN, 7:1 (2017), 82–84
65.	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.

2016
66.	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
67.	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
68.	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

2015
69.	A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18	5 ^[x]
70.	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
71.	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	2 ^[x]

2014
72.	A. R. Alimov, “The Rainwater–Simons weak convergence theorem for the Brown associated norm”, Eurasian Math. J., 5:2 (2014), 126–131	2 ^[x]

2016
73.	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

2014
74.	A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655
75.	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

2012
76.	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	5 ^[x]

2014
77.	A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454

2013
78.	A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, J. Math. Sci., 191:5 (2013), 599–604

2012
79.	A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in the space $C(Q)$”, J. Math. Sci., 185:3 (2012), 360–366
80.	A. R. Alimov, “A Monotone Path Connected Chebyshev Set Is a Sun”, Math. Notes, 91:2 (2012), 290–292
81.	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 ; 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	3 ^[x]

Full list of publications