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.
A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
2.
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. ;
A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of a union of subspaces in asymmetric normed spaces”, Izv. RAN. Ser. Mat. (to appear)
2024
4.
A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
5.
A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259;
6.
A. R. Alimov, I. G. Tsarkov, “Monotonno lineino svyaznye mnozhestva v geometricheskoi teorii priblizheniya i ee prilozheniyakh”, Matematika i teoreticheskie kompyuternye nauki, 22:2 (2024), 30-46
7.
A. R. Alimov, “Balayage theorems for connectedness problems in uniformly convex spaces”, Proc. of Institute of mathematics and mechanics, 50:1 (2024), 53–61;
2023
8.
A. R. Alimov, I. G. Tsarkov, Sovremennaya geometricheskaya teoriya priblizhenii, “OntoPrint”, Moskva, 2023 , 425 pp.
9.
A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31 (2023), 2287–2295
10.
A. R. Alimov, “Strict Protosuns in Asymmetric Spaces of Continuous Functions”, Results in Mathematics, 78 (2023), 95 , 15 pp.
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
12.
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
13.
A. R. Alimov, “Universality theorems for asymmetric spaces”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 26:2 (2023), 2250017 , 11 pp.
A. R Alimov, “Approximative solar properties of sets and local geometry of the unit sphere”, Lobachevskii Journal of Mathematics, 44:12 (2023), 5142–5148
2022
15.
Alexey R. Alimov, Igor' G. Tsarkov, Geometric Approximation Theory, Springer Monographs in Mathematics, Springer, 2022 , xxi+508 pp.
A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
22.
A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
23.
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
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
29.
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
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
2019
33.
A. R. Alimov, “Continuity of the metric projection and local solar properties of sets”, Set-Valued Var. Anal., 27:1 (2019), 213–222
A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
37.
A. R. Alimov, “Singularities of Solutions of the Eikonal Equation”, Differ. Equ., 55:10 (2019), 1311–1316
38.
Alexey R. Alimov, Evgeny V. Shchepin, “Convexity of Suns in Tangent Directions”, J. Convex Anal., 26:4 (2019), 1071–1076
2018
39.
A. R. Alimov, E. V. Shchepin, “Convexity of Chebyshev sets with respect to tangent directions”, Russian Math. Surveys, 73:2 (2018), 366–368
40.
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
41.
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.
42.
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
43.
A. R. Alimov, “On approximative properties of locally Chebyshev sets”, Proc. of Institute of mathematics and mechanics, 44:1 (2018), 36–42
44.
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
45.
A. R. Alimov, “Bounded contractibility of strict suns in three-dimensional spaces”, J. Math. Sci., 250:3 (2020), 385–390
2018
46.
A. R. Alimov, “Lokalno chebyshevskie mnozhestva”, Vestnik Filiala Moskovskogo gosudarstvennogo universiteta imeni M.V. Lomonosova v gorode Dushanbe, 2:1 (2018), 5-11
2017
47.
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
48.
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
49.
A. R. Alimov, I. G. Tsarkov, Geometricheskaya teoriya priblizhenii. Chast I. Klassicheskie ponyatiya i konstruktsii priblizheniya mnozhestvami, OntoPrint, Moskva, 2017 , 346 pp.
50.
A. R. Alimov, “O sootnoshenii mezhdu klassami solnts v nesimmetrichno normirovannykh prostranstvakh”, Trudy NIISI RAN, 7:1 (2017), 82–84
51.
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
52.
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
53.
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
54.
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
55.
A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
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
57.
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
A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
2013
64.
A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, J. Math. Sci., 191:5 (2013), 599–604
2012
65.
A. R. Alimov, “Monotone path-connectedness of $R$-weakly convex sets in the space $C(Q)$”, J. Math. Sci., 185:3 (2012), 360–366
66.
A. R. Alimov, “A Monotone Path Connected Chebyshev Set Is a Sun”, Math. Notes, 91:2 (2012), 290–292
67.
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