## Alimov, Alexey R.

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 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
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### 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
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### 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
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### 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)

### 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 1350.41031
Alimov, A. R.; Tsar’kov, I. G.
2016
Monotone path-connectedness of Chebyshev sets in the space $$C(Q)$$. Zbl 1147.41011
Alimov, A. R.
2006
Connectedness and other geometric properties of suns and Chebyshev sets. Zbl 1361.46012
Alimov, Alexey R.; Tsar’kov, I. G.
2016
On the structure of the complements of Chebyshev sets. Zbl 1099.41501
Alimov, A. R.
2001
Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces. Zbl 1303.41018
Alimov, A. R.
2014
Chebyshev centres, Jung constants, and their applications. Zbl 1435.41028
Alimov, A. R.; Tsar’kov, I. G.
2019
Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces. Zbl 1310.41024
Alimov, A. R.
2014
The Banach-Mazur theorem for spaces with nonsymmetric distance. Zbl 1064.46067
Alimov, A. R.
2003
Selections of the metric projection operator and strict solarity of sets with continuous metric projection. Zbl 1426.41039
Alimov, Alexey R.
2017
Convexity of Chebyshev sets with respect to tangent directions. Zbl 1404.41009
Alimov, Alekseĭ R.; Shchepin, Evgeniĭ V.
2018
The geometric structure of Chebyshev sets in $$\ell^\infty(n)$$. Zbl 1087.41027
Alimov, A. R.
2005
Monotone path-connectedness of Chebyshev sets in three-dimensional spaces. Zbl 1472.41019
Alimov, Alexey R.; Bednov, Borislav B.
2021
Preservation of approximative properties of subsets of Chebyshev sets and suns in $$\ell^\infty(n)$$. Zbl 1157.41003
Alimov, A. R.
2006
Separation of convex sets by extreme hyperplanes. Zbl 1280.52022
Alimov, A. R.; Protasov, V. Yu.
2013
A geometric characterization of strict suns in the space $$l^\infty(n)$$. Zbl 1027.46503
Alimov, A. R.
2001
Sets with external Chebyshev layer. Zbl 0988.41019
Alimov, A. R.; Karlov, M. I.
2001
A monotone path connected Chebyshev set is a sun. Zbl 1285.41018
Alimov, A. R.
2012
Connectedness of suns in the space $$c_ 0$$. Zbl 1095.46009
Alimov, A. R.
2005
Preservation of approximative properties of Chebyshev sets and suns in a plane. Zbl 1304.41018
Alimov, A. R.
2008
Convexity of suns in tangent directions. Zbl 1441.46012
Alimov, Alexey R.; Shchepin, Evgeny V.
2019
Smoothness of subspace sections of the unit balls of $$C(Q)$$ and $$L^1$$. Zbl 1464.46022
Alimov, A. R.; Tsar’kov, I. G.
2021
Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns. Zbl 1489.41020
Alimov, A. R.; Tsar’kov, I. G.
2021
Convexity of Chebyshev sets contained in a subspace. Zbl 1095.46008
Alimov, A. R.
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 1423.41050
Alimov, A. R.
2019
Selections of the best and near-best approximation operators and solarity. Zbl 1423.41041
Alimov, Alekseĭ R.
2018
Chebyshev compact sets in the plane. Zbl 0952.41016
Alimov, A. R.
1997
On finite-dimensional Banach spaces in which suns are connected. Zbl 1474.46027
Alimov, Alekseĭ Rostislavovich
2015
Solarity of sets in max-approximation problems. Zbl 1442.41010
Alimov, Alexey R.
2019
Local solarity of suns in normed linear spaces. Zbl 1314.46018
Alimov, A. R.
2014
Monotone path-connectedness of $$R$$-weakly convex sets in spaces with linear ball embedding. Zbl 1269.46009
Alimov, A. R.
2012
Singularities of solutions of the eikonal equation. Zbl 1439.35498
Alimov, A. R.
2019
Chebyshev set’s complement. Zbl 0866.46006
Alimov, A. R.
1996
On approximative properties of locally Chebyshev sets. Zbl 1405.41017
Alimov, Alexey R.
2018
Characterisations of Chebyshev sets in $$c_{0}$$. Zbl 1065.41056
Alimov, Alexey R.
2004
A number of connected components of sun’s complement. Zbl 0860.46007
Alimov, A. R.
1995
In memoriam: Hubert A. Berens (1936–2015). Zbl 1319.01021
Alimov, 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
2015
A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. Zbl 1376.46014
Alimov, Alexey R.
2017
Ball-complete sets and solar properties of sets in asymmetric spaces. Zbl 07490197
Alimov, Alexey R.; Tsar’kov, Igor’ G.
2022
$$\mathring{B}$$-complete sets: approximative and structural properties. Zbl 07538026
Alimov, A. R.; Tsarkov, I. G.
2022
Solarity of Chebyshev sets in dual spaces and uniquely remotal sets. Zbl 1470.41027
Alimov, A. R.
2021
Solstice property for a system of 2-spaces. Zbl 0914.46011
Alimov, A. R.
1998
Bounded contractibility of strict suns in three-dimensional spaces. Zbl 1452.46010
Alimov, A. R.
2020
Characterization of sets with continuous metric projection in the space $$\ell^\infty_n$$. Zbl 1452.41016
Alimov, A. R.
2020
Mazur spaces and 4.3-intersection property of $$(BM)$$-spaces. Zbl 1361.46011
Alimov, Alexey R.
2016
The Rainwater-Simons weak convergence theorem for the Brown associated norm. Zbl 1326.46006
Alimov, A. R.
2014
Ball-complete sets and solar properties of sets in asymmetric spaces. Zbl 07490197
Alimov, Alexey R.; Tsar&rsquo;kov, Igor&rsquo; G.
2022
$$\mathring{B}$$-complete sets: approximative and structural properties. Zbl 07538026
Alimov, A. R.; Tsarkov, I. G.
2022
Monotone path-connectedness of Chebyshev sets in three-dimensional spaces. Zbl 1472.41019
Alimov, Alexey R.; Bednov, Borislav B.
2021
Smoothness of subspace sections of the unit balls of $$C(Q)$$ and $$L^1$$. Zbl 1464.46022
Alimov, A. R.; Tsar&rsquo;kov, I. G.
2021
Approximatively compact sets in asymmetric Efimov-Stechkin spaces and convexity of almost suns. Zbl 1489.41020
Alimov, A. R.; Tsar&rsquo;kov, I. G.
2021
Solarity of Chebyshev sets in dual spaces and uniquely remotal sets. Zbl 1470.41027
Alimov, A. R.
2021
Bounded contractibility of strict suns in three-dimensional spaces. Zbl 1452.46010
Alimov, A. R.
2020
Characterization of sets with continuous metric projection in the space $$\ell^\infty_n$$. Zbl 1452.41016
Alimov, A. R.
2020
Chebyshev centres, Jung constants, and their applications. Zbl 1435.41028
Alimov, A. R.; Tsar&rsquo;kov, I. G.
2019
Convexity of suns in tangent directions. Zbl 1441.46012
Alimov, Alexey R.; Shchepin, Evgeny V.
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 1423.41050
Alimov, A. R.
2019
Solarity of sets in max-approximation problems. Zbl 1442.41010
Alimov, Alexey R.
2019
Singularities of solutions of the eikonal equation. Zbl 1439.35498
Alimov, A. R.
2019
Convexity of Chebyshev sets with respect to tangent directions. Zbl 1404.41009
Alimov, Alekseĭ R.; Shchepin, Evgeniĭ V.
2018
Selections of the best and near-best approximation operators and solarity. Zbl 1423.41041
Alimov, Alekseĭ R.
2018
On approximative properties of locally Chebyshev sets. Zbl 1405.41017
Alimov, Alexey R.
2018
Selections of the metric projection operator and strict solarity of sets with continuous metric projection. Zbl 1426.41039
Alimov, Alexey R.
2017
A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. Zbl 1376.46014
Alimov, Alexey R.
2017
Connectedness and solarity in problems of best and near-best approximation. Zbl 1350.41031
Alimov, A. R.; Tsar&rsquo;kov, I. G.
2016
Connectedness and other geometric properties of suns and Chebyshev sets. Zbl 1361.46012
Alimov, Alexey R.; Tsar&rsquo;kov, I. G.
2016
Mazur spaces and 4.3-intersection property of $$(BM)$$-spaces. Zbl 1361.46011
Alimov, Alexey R.
2016
On finite-dimensional Banach spaces in which suns are connected. Zbl 1474.46027
Alimov, Alekseĭ Rostislavovich
2015
In memoriam: Hubert A. Berens (1936–2015). Zbl 1319.01021
Alimov, 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
2015
Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces. Zbl 1303.41018
Alimov, A. R.
2014
Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces. Zbl 1310.41024
Alimov, A. R.
2014
Local solarity of suns in normed linear spaces. Zbl 1314.46018
Alimov, A. R.
2014
The Rainwater-Simons weak convergence theorem for the Brown associated norm. Zbl 1326.46006
Alimov, A. R.
2014
Separation of convex sets by extreme hyperplanes. Zbl 1280.52022
Alimov, A. R.; Protasov, V. Yu.
2013
A monotone path connected Chebyshev set is a sun. Zbl 1285.41018
Alimov, A. R.
2012
Monotone path-connectedness of $$R$$-weakly convex sets in spaces with linear ball embedding. Zbl 1269.46009
Alimov, A. R.
2012
Preservation of approximative properties of Chebyshev sets and suns in a plane. Zbl 1304.41018
Alimov, A. R.
2008
Monotone path-connectedness of Chebyshev sets in the space $$C(Q)$$. Zbl 1147.41011
Alimov, A. R.
2006
Preservation of approximative properties of subsets of Chebyshev sets and suns in $$\ell^\infty(n)$$. Zbl 1157.41003
Alimov, A. R.
2006
The geometric structure of Chebyshev sets in $$\ell^\infty(n)$$. Zbl 1087.41027
Alimov, A. R.
2005
Connectedness of suns in the space $$c_ 0$$. Zbl 1095.46009
Alimov, A. R.
2005
Convexity of Chebyshev sets contained in a subspace. Zbl 1095.46008
Alimov, A. R.
2005
Characterisations of Chebyshev sets in $$c_{0}$$. Zbl 1065.41056
Alimov, Alexey R.
2004
The Banach-Mazur theorem for spaces with nonsymmetric distance. Zbl 1064.46067
Alimov, A. R.
2003
On the structure of the complements of Chebyshev sets. Zbl 1099.41501
Alimov, A. R.
2001
A geometric characterization of strict suns in the space $$l^\infty(n)$$. Zbl 1027.46503
Alimov, A. R.
2001
Sets with external Chebyshev layer. Zbl 0988.41019
Alimov, A. R.; Karlov, M. I.
2001
Solstice property for a system of 2-spaces. Zbl 0914.46011
Alimov, A. R.
1998
Chebyshev compact sets in the plane. Zbl 0952.41016
Alimov, A. R.
1997
Chebyshev set’s complement. Zbl 0866.46006
Alimov, A. R.
1996
A number of connected components of sun’s complement. Zbl 0860.46007
Alimov, A. R.
1995
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### 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
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### 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
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### 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)