Edit Profile (opens in new tab) Alimov, Alexey R. Compute Distance To: Compute Author ID: alimov.alexey-r Published as: Alimov, A. R.; Alimov, Alexey R.; Alimov, Alekseĭ R.; Alimov, Alexey; Alimov, Alekseĭ Rostislavovich more...less External Links: MGP · ORCID · Math-Net.Ru Documents Indexed: 59 Publications since 1995, including 2 Books Reviewing Activity: 297 Reviews Co-Authors: 22 Co-Authors with 21 Joint Publications 726 Co-Co-Authors all top 5 Co-Authors 38 single-authored 11 Tsar’kov, Igor’ Germanovich 3 Shchepin, Evgenij V. 1 Bednov, Borislav Borisovich 1 Berdysheva, Elena E. 1 Berens, Hubert Anton 1 Borovkov, Aleksandr Alekseevich 1 Bukhzhalev, Evgeny E. 1 Butzer, Paul Leo 1 Dahmen, Wolfgang A. 1 DeVore, Ron 1 Filbir, Frank-Dieter 1 Jetter, Kurt 1 Karlov, M. I. 1 Mhaskar, Hrushikesh N. 1 Nevai, Paul G. 1 Protasov, Vladimir Yu. 1 Sauer, Tomas 1 Schumaker, Larry L. 1 Sommer, Manfred 1 Strauss, Hans 1 Xu, Yuan 1 zu Castell, Wolfgang all top 5 Serials 7 Mathematical Notes 5 Russian Mathematical Surveys 5 Journal of Mathematical Sciences (New York) 4 Journal of Approximation Theory 3 East Journal on Approximations 3 Sbornik: Mathematics 3 Izvestiya: Mathematics 3 Eurasian Mathematical Journal 2 Moscow University Mathematics Bulletin 2 Theory of Probability and its Applications 2 Functional Analysis and its Applications 2 Siberian Mathematical Journal 2 Lobachevskii Journal of Mathematics 2 Set-Valued and Variational Analysis 2 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Results in Mathematics 1 Russian Journal of Mathematical Physics 1 Turkish Journal of Mathematics 1 Journal of Convex Analysis 1 Doklady Mathematics 1 Differential Equations 1 Proceedings of Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan 1 Encyclopedia of Mathematics and Its Applications 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Fixed Point Theory and Applications 1 Springer Monographs in Mathematics all top 5 Fields 45 Approximations and expansions (41-XX) 34 Functional analysis (46-XX) 10 Convex and discrete geometry (52-XX) 9 General topology (54-XX) 3 History and biography (01-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 45 Publications have been cited 261 times in 88 Documents Cited by ▼ Year ▼ Connectedness and solarity in problems of best and near-best approximation. Zbl 1350.41031Alimov, A. R.; Tsar’kov, I. G. 46 2016 Monotone path-connectedness of Chebyshev sets in the space \(C(Q)\). Zbl 1147.41011Alimov, A. R. 19 2006 Connectedness and other geometric properties of suns and Chebyshev sets. Zbl 1361.46012Alimov, Alexey R.; Tsar’kov, I. G. 15 2016 On the structure of the complements of Chebyshev sets. Zbl 1099.41501Alimov, A. R. 14 2001 Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces. Zbl 1303.41018Alimov, A. R. 14 2014 Chebyshev centres, Jung constants, and their applications. Zbl 1435.41028Alimov, A. R.; Tsar’kov, I. G. 12 2019 Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces. Zbl 1310.41024Alimov, A. R. 8 2014 The Banach-Mazur theorem for spaces with nonsymmetric distance. Zbl 1064.46067Alimov, A. R. 8 2003 Selections of the metric projection operator and strict solarity of sets with continuous metric projection. Zbl 1426.41039Alimov, Alexey R. 7 2017 Convexity of Chebyshev sets with respect to tangent directions. Zbl 1404.41009Alimov, Alekseĭ R.; Shchepin, Evgeniĭ V. 7 2018 The geometric structure of Chebyshev sets in \(\ell^\infty(n)\). Zbl 1087.41027Alimov, A. R. 7 2005 Monotone path-connectedness of Chebyshev sets in three-dimensional spaces. Zbl 1472.41019Alimov, Alexey R.; Bednov, Borislav B. 6 2021 Preservation of approximative properties of subsets of Chebyshev sets and suns in \(\ell^\infty(n)\). Zbl 1157.41003Alimov, A. R. 6 2006 Separation of convex sets by extreme hyperplanes. Zbl 1280.52022Alimov, A. R.; Protasov, V. Yu. 6 2013 A geometric characterization of strict suns in the space \(l^\infty(n)\). Zbl 1027.46503Alimov, A. R. 5 2001 Sets with external Chebyshev layer. Zbl 0988.41019Alimov, A. R.; Karlov, M. I. 5 2001 A monotone path connected Chebyshev set is a sun. Zbl 1285.41018Alimov, A. R. 5 2012 Connectedness of suns in the space \(c_ 0\). Zbl 1095.46009Alimov, A. R. 5 2005 Preservation of approximative properties of Chebyshev sets and suns in a plane. Zbl 1304.41018Alimov, A. R. 5 2008 Convexity of suns in tangent directions. Zbl 1441.46012Alimov, Alexey R.; Shchepin, Evgeny V. 4 2019 Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\). Zbl 1464.46022Alimov, A. R.; Tsar’kov, I. G. 4 2021 Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns. Zbl 1489.41020Alimov, A. R.; Tsar’kov, I. G. 4 2021 Convexity of Chebyshev sets contained in a subspace. Zbl 1095.46008Alimov, A. R. 4 2005 Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties. Zbl 1423.41050Alimov, A. R. 3 2019 Selections of the best and near-best approximation operators and solarity. Zbl 1423.41041Alimov, Alekseĭ R. 3 2018 Chebyshev compact sets in the plane. Zbl 0952.41016Alimov, A. R. 3 1997 On finite-dimensional Banach spaces in which suns are connected. Zbl 1474.46027Alimov, Alekseĭ Rostislavovich 3 2015 Solarity of sets in max-approximation problems. Zbl 1442.41010Alimov, Alexey R. 3 2019 Local solarity of suns in normed linear spaces. Zbl 1314.46018Alimov, A. R. 3 2014 Monotone path-connectedness of \(R\)-weakly convex sets in spaces with linear ball embedding. Zbl 1269.46009Alimov, A. R. 3 2012 Singularities of solutions of the eikonal equation. Zbl 1439.35498Alimov, A. R. 2 2019 Chebyshev set’s complement. Zbl 0866.46006Alimov, A. R. 2 1996 On approximative properties of locally Chebyshev sets. Zbl 1405.41017Alimov, Alexey R. 2 2018 Characterisations of Chebyshev sets in \(c_{0}\). Zbl 1065.41056Alimov, Alexey R. 2 2004 A number of connected components of sun’s complement. Zbl 0860.46007Alimov, A. R. 2 1995 In memoriam: Hubert A. Berens (1936–2015). Zbl 1319.01021Alimov, Alexey; Berdysheva, Elena; Butzer, Paul; zu Castell, Wolfgang; Dahmen, Wolfgang; DeVore, Ron; Filbir, Frank; Jetter, Kurt; Mhaskar, Hrushikesh; Nevai, Paul; Sauer, Tomas; Schumaker, Larry; Sommer, Manfred; Strauss, Hans; Xu, Yuan 2 2015 A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. Zbl 1376.46014Alimov, Alexey R. 2 2017 Ball-complete sets and solar properties of sets in asymmetric spaces. Zbl 07490197Alimov, Alexey R.; Tsar’kov, Igor’ G. 2 2022 \(\mathring{B}\)-complete sets: approximative and structural properties. Zbl 07538026Alimov, A. R.; Tsarkov, I. G. 2 2022 Solarity of Chebyshev sets in dual spaces and uniquely remotal sets. Zbl 1470.41027Alimov, A. R. 1 2021 Solstice property for a system of 2-spaces. Zbl 0914.46011Alimov, A. R. 1 1998 Bounded contractibility of strict suns in three-dimensional spaces. Zbl 1452.46010Alimov, A. R. 1 2020 Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\). Zbl 1452.41016Alimov, A. R. 1 2020 Mazur spaces and 4.3-intersection property of \((BM)\)-spaces. Zbl 1361.46011Alimov, Alexey R. 1 2016 The Rainwater-Simons weak convergence theorem for the Brown associated norm. Zbl 1326.46006Alimov, A. R. 1 2014 Ball-complete sets and solar properties of sets in asymmetric spaces. Zbl 07490197Alimov, Alexey R.; Tsar’kov, Igor’ G. 2 2022 \(\mathring{B}\)-complete sets: approximative and structural properties. Zbl 07538026Alimov, A. R.; Tsarkov, I. G. 2 2022 Monotone path-connectedness of Chebyshev sets in three-dimensional spaces. Zbl 1472.41019Alimov, Alexey R.; Bednov, Borislav B. 6 2021 Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\). Zbl 1464.46022Alimov, A. R.; Tsar’kov, I. G. 4 2021 Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns. Zbl 1489.41020Alimov, A. R.; Tsar’kov, I. G. 4 2021 Solarity of Chebyshev sets in dual spaces and uniquely remotal sets. Zbl 1470.41027Alimov, A. R. 1 2021 Bounded contractibility of strict suns in three-dimensional spaces. Zbl 1452.46010Alimov, A. R. 1 2020 Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\). Zbl 1452.41016Alimov, A. R. 1 2020 Chebyshev centres, Jung constants, and their applications. Zbl 1435.41028Alimov, A. R.; Tsar’kov, I. G. 12 2019 Convexity of suns in tangent directions. Zbl 1441.46012Alimov, Alexey R.; Shchepin, Evgeny V. 4 2019 Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties. Zbl 1423.41050Alimov, A. R. 3 2019 Solarity of sets in max-approximation problems. Zbl 1442.41010Alimov, Alexey R. 3 2019 Singularities of solutions of the eikonal equation. Zbl 1439.35498Alimov, A. R. 2 2019 Convexity of Chebyshev sets with respect to tangent directions. Zbl 1404.41009Alimov, Alekseĭ R.; Shchepin, Evgeniĭ V. 7 2018 Selections of the best and near-best approximation operators and solarity. Zbl 1423.41041Alimov, Alekseĭ R. 3 2018 On approximative properties of locally Chebyshev sets. Zbl 1405.41017Alimov, Alexey R. 2 2018 Selections of the metric projection operator and strict solarity of sets with continuous metric projection. Zbl 1426.41039Alimov, Alexey R. 7 2017 A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. Zbl 1376.46014Alimov, Alexey R. 2 2017 Connectedness and solarity in problems of best and near-best approximation. Zbl 1350.41031Alimov, A. R.; Tsar’kov, I. G. 46 2016 Connectedness and other geometric properties of suns and Chebyshev sets. Zbl 1361.46012Alimov, Alexey R.; Tsar’kov, I. G. 15 2016 Mazur spaces and 4.3-intersection property of \((BM)\)-spaces. Zbl 1361.46011Alimov, Alexey R. 1 2016 On finite-dimensional Banach spaces in which suns are connected. Zbl 1474.46027Alimov, Alekseĭ Rostislavovich 3 2015 In memoriam: Hubert A. Berens (1936–2015). Zbl 1319.01021Alimov, Alexey; Berdysheva, Elena; Butzer, Paul; zu Castell, Wolfgang; Dahmen, Wolfgang; DeVore, Ron; Filbir, Frank; Jetter, Kurt; Mhaskar, Hrushikesh; Nevai, Paul; Sauer, Tomas; Schumaker, Larry; Sommer, Manfred; Strauss, Hans; Xu, Yuan 2 2015 Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces. Zbl 1303.41018Alimov, A. R. 14 2014 Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces. Zbl 1310.41024Alimov, A. R. 8 2014 Local solarity of suns in normed linear spaces. Zbl 1314.46018Alimov, A. R. 3 2014 The Rainwater-Simons weak convergence theorem for the Brown associated norm. Zbl 1326.46006Alimov, A. R. 1 2014 Separation of convex sets by extreme hyperplanes. Zbl 1280.52022Alimov, A. R.; Protasov, V. Yu. 6 2013 A monotone path connected Chebyshev set is a sun. Zbl 1285.41018Alimov, A. R. 5 2012 Monotone path-connectedness of \(R\)-weakly convex sets in spaces with linear ball embedding. Zbl 1269.46009Alimov, A. R. 3 2012 Preservation of approximative properties of Chebyshev sets and suns in a plane. Zbl 1304.41018Alimov, A. R. 5 2008 Monotone path-connectedness of Chebyshev sets in the space \(C(Q)\). Zbl 1147.41011Alimov, A. R. 19 2006 Preservation of approximative properties of subsets of Chebyshev sets and suns in \(\ell^\infty(n)\). Zbl 1157.41003Alimov, A. R. 6 2006 The geometric structure of Chebyshev sets in \(\ell^\infty(n)\). Zbl 1087.41027Alimov, A. R. 7 2005 Connectedness of suns in the space \(c_ 0\). Zbl 1095.46009Alimov, A. R. 5 2005 Convexity of Chebyshev sets contained in a subspace. Zbl 1095.46008Alimov, A. R. 4 2005 Characterisations of Chebyshev sets in \(c_{0}\). Zbl 1065.41056Alimov, Alexey R. 2 2004 The Banach-Mazur theorem for spaces with nonsymmetric distance. Zbl 1064.46067Alimov, A. R. 8 2003 On the structure of the complements of Chebyshev sets. Zbl 1099.41501Alimov, A. R. 14 2001 A geometric characterization of strict suns in the space \(l^\infty(n)\). Zbl 1027.46503Alimov, A. R. 5 2001 Sets with external Chebyshev layer. Zbl 0988.41019Alimov, A. R.; Karlov, M. I. 5 2001 Solstice property for a system of 2-spaces. Zbl 0914.46011Alimov, A. R. 1 1998 Chebyshev compact sets in the plane. Zbl 0952.41016Alimov, A. R. 3 1997 Chebyshev set’s complement. Zbl 0866.46006Alimov, A. R. 2 1996 A number of connected components of sun’s complement. Zbl 0860.46007Alimov, A. R. 2 1995 all cited Publications top 5 cited Publications all top 5 Cited by 45 Authors 31 Alimov, Alexey R. 31 Tsar’kov, Igor’ Germanovich 4 Alegre, Carmen 4 Ivanov, Grigorii E. 4 Romaguera Bonilla, Salvador 4 Shchepin, Evgenij V. 3 Lebedev, Pavel Dmitrievich 3 Lopushanski, Mariana S. 3 Sánchez-Pérez, Enrique Alfonso 2 Balestro, Vitor 2 Bednov, Borislav Borisovich 2 Butzer, Paul Leo 2 Dudov, Sergeĭ Ivanovich 2 García-Raffi, Luis M. 2 Martini, Horst 2 Shklyaev, Konstantin S. 2 Stens, Rudolf L. 2 Uspenskiĭ, Aleksandr Aleksandrovich 2 Valero, Oscar 1 Abramova, Veronika Valer’evna 1 Alimov, A. P. 1 Balashov, Maxim Viktorovich 1 Chelidze, George Z. 1 Cobzaş, Ştefan 1 Danelia, A. N. 1 Daptari, Soumitra 1 Ferrando, Irene 1 Graev, Mark Iosifovich 1 Kozko, Artem Ivanovich 1 Lin, Fucai 1 Lin, Shou 1 Liu, Chuan 1 Nath, Triloki 1 Nikonorov, Yurii Gennadyevich 1 Nikonorova, Yulia V. 1 Osiptsev, Mikhaĭl Anatol’evich 1 Palin, Vladimir Vladimirovich 1 Paul, Tanmoy 1 Polovinkin, Evgenii Sergeevich 1 Protasov, Vladimir Yu. 1 Suladze, M. Z. 1 Teixeira, Ralph Costa 1 Ushakov, Vladimir Nikolaevich 1 Veeramani, P. 1 Vershik, Anatoliĭ Moiseevich all top 5 Cited in 32 Serials 16 Mathematical Notes 11 Journal of Mathematical Sciences (New York) 6 Russian Journal of Mathematical Physics 5 Sbornik: Mathematics 4 Moscow University Mathematics Bulletin 3 Russian Mathematical Surveys 3 Journal of Approximation Theory 3 Topology and its Applications 3 Izvestiya: Mathematics 3 Lobachevskii Journal of Mathematics 3 Set-Valued and Variational Analysis 2 Functional Analysis and its Applications 2 Results in Mathematics 2 Siberian Mathematical Journal 2 Acta Mathematica Hungarica 2 Journal of Convex Analysis 2 Doklady Mathematics 2 Proceedings of the Steklov Institute of Mathematics 1 Fuzzy Sets and Systems 1 Numerical Functional Analysis and Optimization 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Russian Mathematics 1 The Journal of Analysis 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Differential Equations 1 Journal of Fixed Point Theory and Applications 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Eurasian Mathematical Journal 1 Chelyabinskiĭ Fiziko-Matematicheskiĭ Zhurnal 1 Vestnik Rossiĭskikh Universitetov. Matematika 1 Sampling Theory, Signal Processing, and Data Analysis all top 5 Cited in 21 Fields 61 Approximations and expansions (41-XX) 47 Functional analysis (46-XX) 29 General topology (54-XX) 12 Convex and discrete geometry (52-XX) 6 Partial differential equations (35-XX) 5 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Operations research, mathematical programming (90-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 History and biography (01-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) Citations by Year