Alimov, A. R. Balayage theorems for connectedness problems in uniformly convex spaces. (English) Zbl 07868789 Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 50, No. 1, 53-61 (2024). Reviewer: Stefan Cobzaş (Cluj-Napoca) MSC: 41A65 46B20 46N10 PDFBibTeX XMLCite \textit{A. R. Alimov}, Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 50, No. 1, 53--61 (2024; Zbl 07868789) Full Text: DOI
Alimov, A. R.; Tsar’kov, I. G. Chebyshev unions of planes, and their approximative and geometric properties. (English) Zbl 07806805 J. Approx. Theory 298, Article ID 106009, 12 p. (2024). MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, J. Approx. Theory 298, Article ID 106009, 12 p. (2024; Zbl 07806805) Full Text: DOI
Alimov, A. R. On local properties of spaces implying monotone path-connectedness of suns. (English) Zbl 1535.41031 J. Anal. 31, No. 3, 2287-2295 (2023). MSC: 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, J. Anal. 31, No. 3, 2287--2295 (2023; Zbl 1535.41031) Full Text: DOI
Alimov, Alexey R.; Tsar’kov, Igor’ G. Max-solar properties of sets in normed and asymmetrically normed spaces. (English) Zbl 1515.41020 J. Convex Anal. 30, No. 1, 159-174 (2023). Reviewer: Sorin Gheorghe Gal (Oradea) MSC: 41A65 41A28 52A21 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, J. Convex Anal. 30, No. 1, 159--174 (2023; Zbl 1515.41020) Full Text: Link
Alimov, A. R.; Tsar’kov, I. G. Classical problems of rational approximation. (English. Russian original) Zbl 1528.41073 Dokl. Math. 106, No. 2, 305-307 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 5-8 (2022). MSC: 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, Dokl. Math. 106, No. 2, 305--307 (2022; Zbl 1528.41073); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 506, 5--8 (2022) Full Text: DOI
Alimov, Alexey R.; Tsar’kov, Igor’ G. Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces. (English) Zbl 1515.41019 Set-Valued Var. Anal. 30, No. 3, 1233-1245 (2022). MSC: 41A65 41A50 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, Set-Valued Var. Anal. 30, No. 3, 1233--1245 (2022; Zbl 1515.41019) Full Text: DOI
Alimov, A. R.; Tsarkov, I. G. \(\mathring{B}\)-complete sets: approximative and structural properties. (English. Russian original) Zbl 1506.46017 Sib. Math. J. 63, No. 3, 412-420 (2022); translation from Sib. Mat. Zh. 63, No. 3, 500-509 (2022). MSC: 46B20 41A65 46B99 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsarkov}, Sib. Math. J. 63, No. 3, 412--420 (2022; Zbl 1506.46017); translation from Sib. Mat. Zh. 63, No. 3, 500--509 (2022) Full Text: DOI
Alimov, Alexey R.; Tsar’kov, Igor’ G. Geometric approximation theory. (English) Zbl 1494.41001 Springer Monographs in Mathematics. Cham: Springer (ISBN 978-3-030-90950-5/hbk; 978-3-030-90953-6/pbk; 978-3-030-90951-2/ebook). xxi, 508 p. (2022). Reviewer: Costică Moroşanu (Iaşi) MSC: 41-01 41-02 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, Geometric approximation theory. Cham: Springer (2022; Zbl 1494.41001) Full Text: DOI
Alimov, Alexey R.; Bednov, Borislav B. Monotone path-connectedness of Chebyshev sets in three-dimensional spaces. (English. Russian original) Zbl 1472.41019 Sb. Math. 212, No. 5, 636-654 (2021); translation from Mat. Sb. 212, No. 5, 37-57 (2021). Reviewer: Daniel Cárdenas Morales (Jaén) MSC: 41A65 41A50 46A55 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{B. B. Bednov}, Sb. Math. 212, No. 5, 636--654 (2021; Zbl 1472.41019); translation from Mat. Sb. 212, No. 5, 37--57 (2021) Full Text: DOI
Alimov, A. R. Solarity of Chebyshev sets in dual spaces and uniquely remotal sets. (English) Zbl 1470.41027 Lobachevskii J. Math. 42, No. 4, 785-790 (2021). Reviewer: Richard A. Zalik (Auburn) MSC: 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Lobachevskii J. Math. 42, No. 4, 785--790 (2021; Zbl 1470.41027) Full Text: DOI
Alimov, A. R.; Tsar’kov, I. G. Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\). (English) Zbl 1464.46022 J. Approx. Theory 265, Article ID 105552, 8 p. (2021). Reviewer: Elói M. Galego (São Paulo) MSC: 46E15 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, J. Approx. Theory 265, Article ID 105552, 8 p. (2021; Zbl 1464.46022) Full Text: DOI
Alimov, A. R. Geometric structure of Chebyshev sets and suns in three-dimensional spaces with a cylindrical norm. (English. Russian original) Zbl 1465.41011 Mosc. Univ. Math. Bull. 75, No. 5, 209-215 (2020); translation from Vestn. Mosk. Univ., Ser. I 75, No. 5, 26-32 (2020). Reviewer: Sorin-Mihai Grad (Wien) MSC: 41A99 52A15 54C50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Mosc. Univ. Math. Bull. 75, No. 5, 209--215 (2020; Zbl 1465.41011); translation from Vestn. Mosk. Univ., Ser. I 75, No. 5, 26--32 (2020) Full Text: DOI
Alimov, A. R. Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\). (English. Russian original) Zbl 1452.41016 Math. Notes 108, No. 3, 309-317 (2020); translation from Mat. Zametki 108, No. 3, 323-333 (2020). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Math. Notes 108, No. 3, 309--317 (2020; Zbl 1452.41016); translation from Mat. Zametki 108, No. 3, 323--333 (2020) Full Text: DOI
Alimov, A. R. Bounded contractibility of strict suns in three-dimensional spaces. (English. Russian original) Zbl 1452.46010 J. Math. Sci., New York 250, No. 3, 385-390 (2020); translation from Fundam. Prikl. Mat. 22, No. 1, 3-11 (2018). Reviewer: Stefan Cobzaş (Cluj-Napoca) (MR3914355) MSC: 46B20 41A65 52A30 54C65 54C55 55M15 PDFBibTeX XMLCite \textit{A. R. Alimov}, J. Math. Sci., New York 250, No. 3, 385--390 (2020; Zbl 1452.46010); translation from Fundam. Prikl. Mat. 22, No. 1, 3--11 (2018) Full Text: DOI
Alimov, A. R.; Tsar’kov, I. G. Chebyshev centres, Jung constants, and their applications. (English. Russian original) Zbl 1435.41028 Russ. Math. Surv. 74, No. 5, 775-849 (2019); translation from Usp. Mat. Nauk 74, No. 5, 3-82 (2019). Reviewer: T.S.S.R.K. Rao (Bangalore) MSC: 41A46 41A28 41A65 46B20 54C60 54C65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, Russ. Math. Surv. 74, No. 5, 775--849 (2019; Zbl 1435.41028); translation from Usp. Mat. Nauk 74, No. 5, 3--82 (2019) Full Text: DOI
Alimov, Alexey R.; Shchepin, Evgeny V. Convexity of suns in tangent directions. (English) Zbl 1441.46012 J. Convex Anal. 26, No. 4, 1071-1076 (2019). MSC: 46B20 41A50 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{E. V. Shchepin}, J. Convex Anal. 26, No. 4, 1071--1076 (2019; Zbl 1441.46012) Full Text: Link
Alimov, A. R.; Shchepin, E. V. Convexity of suns in tangent directions. (English. Russian original) Zbl 1427.46008 Dokl. Math. 99, No. 1, 14-15 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 484, No. 2, 131-133 (2019). MSC: 46B20 41A50 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{E. V. Shchepin}, Dokl. Math. 99, No. 1, 14--15 (2019; Zbl 1427.46008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 484, No. 2, 131--133 (2019) Full Text: DOI
Alimov, A. R. 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. (English) Zbl 1423.41050 Set-Valued Var. Anal. 27, No. 1, 213-222 (2019). Reviewer: Andrei Sipoş (Darmstadt) MSC: 41A65 54C65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Set-Valued Var. Anal. 27, No. 1, 213--222 (2019; Zbl 1423.41050) Full Text: DOI
Alimov, Alekseĭ R. Selections of the best and near-best approximation operators and solarity. (English, Russian) Zbl 1423.41041 Proc. Steklov Inst. Math. 303, 10-17 (2018); translation in Tr. Mat. Inst. Steklova 303, 17-25 (2018). Reviewer: Vasile Postolică (Piatra Neamt) MSC: 41A50 41A28 41A35 PDFBibTeX XMLCite \textit{A. R. Alimov}, Proc. Steklov Inst. Math. 303, 10--17 (2018; Zbl 1423.41041); translation in Tr. Mat. Inst. Steklova 303, 17--25 (2018) Full Text: DOI
Alimov, Alexey R. On approximative properties of locally Chebyshev sets. (English) Zbl 1405.41017 Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 44, No. 1, 36-42 (2018). MSC: 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 44, No. 1, 36--42 (2018; Zbl 1405.41017)
Alimov, Alekseĭ R.; Shchepin, Evgeniĭ V. Convexity of Chebyshev sets with respect to tangent directions. (English. Russian original) Zbl 1404.41009 Russ. Math. Surv. 73, No. 2, 366-368 (2018); translation from Usp. Mat. Nauk 73, No. 2, 185-186 (2018). Reviewer: Neha Malik (New Delhi) MSC: 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{E. V. Shchepin}, Russ. Math. Surv. 73, No. 2, 366--368 (2018; Zbl 1404.41009); translation from Usp. Mat. Nauk 73, No. 2, 185--186 (2018) Full Text: DOI
Alimov, Alexey R. A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. (English. Russian original) Zbl 1376.46014 Sib. Math. J. 58, No. 1, 11-15 (2017); translation from Sib. Mat. Zh. 58, No. 1, 16-21 (2017). Reviewer: Stefan Cobzaş (Cluj-Napoca) MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Sib. Math. J. 58, No. 1, 11--15 (2017; Zbl 1376.46014); translation from Sib. Mat. Zh. 58, No. 1, 16--21 (2017) Full Text: DOI
Alimov, Alexey R.; Tsar’kov, I. G. Connectedness and other geometric properties of suns and Chebyshev sets. (English. Russian original) Zbl 1361.46012 J. Math. Sci., New York 217, No. 6, 683-730 (2016); translation from Fundam. Prikl. Mat. 19, No. 4, 21-91 (2014). MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, J. Math. Sci., New York 217, No. 6, 683--730 (2016; Zbl 1361.46012); translation from Fundam. Prikl. Mat. 19, No. 4, 21--91 (2014) Full Text: DOI
Alimov, A. R.; Tsar’kov, I. G. Connectedness and solarity in problems of best and near-best approximation. (English. Russian original) Zbl 1350.41031 Russ. Math. Surv. 71, No. 1, 1-77 (2016); translation from Usp. Mat. Nauk 71, No. 1, 3-84 (2016). Reviewer: Hüseyin Çakallı (Istanbul) MSC: 41A50 41A65 52A30 54C60 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{I. G. Tsar'kov}, Russ. Math. Surv. 71, No. 1, 1--77 (2016; Zbl 1350.41031); translation from Usp. Mat. Nauk 71, No. 1, 3--84 (2016) Full Text: DOI
Alimov, Alekseĭ Rostislavovich On finite-dimensional Banach spaces in which suns are connected. (English) Zbl 1474.46027 Eurasian Math. J. 6, No. 4, 7-18 (2015). MSC: 46B20 41A50 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Eurasian Math. J. 6, No. 4, 7--18 (2015; Zbl 1474.46027) Full Text: MNR
Alimov, A. R. Convexity of bounded Chebyshev sets in finite-dimensional asymmetrically normed spaces. (Russian. English summary) Zbl 1310.41024 Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 14, No. 4, Part 2, 489-497 (2014). MSC: 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 14, No. 4, Part 2, 489--497 (2014; Zbl 1310.41024) Full Text: MNR
Alimov, A. R. A monotone path connected Chebyshev set is a sun. (English. Russian original) Zbl 1285.41018 Math. Notes 91, No. 2, 290-292 (2012); translation from Mat. Zametki 91, No. 2, 305-307 (2012). Reviewer: Stefan Cobzaş (Cluj-Napoca) MSC: 41A65 41A50 41A52 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, Math. Notes 91, No. 2, 290--292 (2012; Zbl 1285.41018); translation from Mat. Zametki 91, No. 2, 305--307 (2012) Full Text: DOI
Alimov, A. R. Monotone path-connectedness of \(R\)-weakly convex sets in spaces with linear ball embedding. (English) Zbl 1269.46009 Eurasian Math. J. 3, No. 2, 21-30 (2012). MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Eurasian Math. J. 3, No. 2, 21--30 (2012; Zbl 1269.46009) Full Text: MNR
Alimov, A. R. Preservation of approximative properties of Chebyshev sets and suns in a plane. (English. Russian original) Zbl 1304.41018 Mosc. Univ. Math. Bull. 63, No. 5, 198-201 (2008); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 5, 46-49 (2008). MSC: 41A50 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, Mosc. Univ. Math. Bull. 63, No. 5, 198--201 (2008; Zbl 1304.41018); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 5, 46--49 (2008) Full Text: DOI
Alimov, A. R. Monotone path-connectedness of Chebyshev sets in the space \(C(Q)\). (English. Russian original) Zbl 1147.41011 Sb. Math. 197, No. 9, 1259-1272 (2006); translation from Mat. Sb. 197, No. 9, 3-18 (2006). Reviewer: László Leindler (Szeged) MSC: 41A65 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, Sb. Math. 197, No. 9, 1259--1272 (2006; Zbl 1147.41011); translation from Mat. Sb. 197, No. 9, 3--18 (2006) Full Text: DOI
Alimov, A. R. Preservation of approximative properties of subsets of Chebyshev sets and suns in \(\ell^\infty(n)\). (English. Russian original) Zbl 1157.41003 Izv. Math. 70, No. 5, 857-866 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 5, 3-12 (2006). Reviewer: Daniel Wulbert (La Jolla) MSC: 41A50 41A65 52A01 PDFBibTeX XMLCite \textit{A. R. Alimov}, Izv. Math. 70, No. 5, 857--866 (2006; Zbl 1157.41003); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 5, 3--12 (2006) Full Text: DOI
Alimov, A. R. Geometric construction of Chebyshev sets in the spaces \(\ell^\infty(n)\) , \(c_0\) and \(c\). (English. Russian original) Zbl 1104.41016 Russ. Math. Surv. 60, No. 3, 559-574 (2005); translation from Usp. Mat. Nauk 60, No. 3, 169-182 (2005). Reviewer: Costica Mustăţa (Cluj-Napoca) MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Russ. Math. Surv. 60, No. 3, 559--574 (2005; Zbl 1104.41016); translation from Usp. Mat. Nauk 60, No. 3, 169--182 (2005) Full Text: DOI
Alimov, A. R. Connectedness of suns in the space \(c_ 0\). (English. Russian original) Zbl 1095.46009 Izv. Math. 69, No. 4, 651-666 (2005); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 4, 3-18 (2005). Reviewer: Costica Mustăţa (Cluj-Napoca) MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Izv. Math. 69, No. 4, 651--666 (2005; Zbl 1095.46009); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 4, 3--18 (2005) Full Text: DOI
Alimov, A. R. Convexity of Chebyshev sets contained in a subspace. (English. Russian original) Zbl 1095.46008 Math. Notes 78, No. 1, 3-13 (2005); translation from Mat. Zametki 78, No. 1, 3-15 (2005). Reviewer: Costica Mustăţa (Cluj-Napoca) MSC: 46B20 41A65 PDFBibTeX XMLCite \textit{A. R. Alimov}, Math. Notes 78, No. 1, 3--13 (2005; Zbl 1095.46008); translation from Mat. Zametki 78, No. 1, 3--15 (2005) Full Text: DOI
Alimov, A. R. The geometric structure of Chebyshev sets in \(\ell^\infty(n)\). (English. Russian original) Zbl 1087.41027 Funct. Anal. Appl. 39, No. 1, 1-8 (2005); translation from Funkts. Anal. Prilozh. 39, No. 1, 1-10 (2005). Reviewer: D. K. Ugulawa (Tbilisi) MSC: 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov}, Funct. Anal. Appl. 39, No. 1, 1--8 (2005; Zbl 1087.41027); translation from Funkts. Anal. Prilozh. 39, No. 1, 1--10 (2005) Full Text: DOI
Alimov, Alexey R. Characterisations of Chebyshev sets in \(c_{0}\). (English) Zbl 1065.41056 J. Approximation Theory 129, No. 2, 217-229 (2004). Reviewer: Dietrich Braess (Bochum) MSC: 41A65 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, J. Approx. Theory 129, No. 2, 217--229 (2004; Zbl 1065.41056) Full Text: DOI
Alimov, A. R. On the structure of the complements of Chebyshev sets. (English. Russian original) Zbl 1099.41501 Funct. Anal. Appl. 35, No. 3, 176-182 (2001); translation from Funkts. Anal. Prilozh. 35, No. 3, 19-27 (2001). MSC: 41A50 41A65 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, Funct. Anal. Appl. 35, No. 3, 176--182 (2001; Zbl 1099.41501); translation from Funkts. Anal. Prilozh. 35, No. 3, 19--27 (2001) Full Text: DOI
Alimov, A. R.; Karlov, M. I. Sets with external Chebyshev layer. (English. Russian original) Zbl 0988.41019 Math. Notes 69, No. 2, 269-273 (2001); translation from Mat. Zametki 69, No. 2, 303-307 (2001). Reviewer: T.D.Narang (Amritsar) MSC: 41A65 46B28 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{M. I. Karlov}, Math. Notes 69, No. 2, 269--273 (2001; Zbl 0988.41019); translation from Mat. Zametki 69, No. 2, 303--307 (2001) Full Text: DOI
Alimov, A. R.; Berens, H. Examples of Chebyshev sets in matrix spaces. (English) Zbl 0943.41015 J. Approximation Theory 99, No. 1, 44-53 (1999). Reviewer: C.Mustăţa (Cluj-Napoca) MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{A. R. Alimov} and \textit{H. Berens}, J. Approx. Theory 99, No. 1, 44--53 (1999; Zbl 0943.41015) Full Text: DOI
Alimov, A. R. Solstice property for a system of 2-spaces. (English) Zbl 0914.46011 East J. Approx. 4, No. 1, 25-34 (1998). Reviewer: P.Petrov (Sofia) MSC: 46B20 PDFBibTeX XMLCite \textit{A. R. Alimov}, East J. Approx. 4, No. 1, 25--34 (1998; Zbl 0914.46011)
Alimov, A. R. Chebyshev compact sets in the plane. (English. Russian original) Zbl 0952.41016 Proc. Steklov Inst. Math. 219, 2-19 (1997); translation from Tr. Mat. Inst. Steklova 219, 8-26 (1997). Reviewer: T.V.Tonev (Missoula) MSC: 41A50 46B99 PDFBibTeX XML
Alimov, A. R. Chebyshev set’s complement. (English) Zbl 0866.46006 East J. Approx. 2, No. 2, 215-232 (1996). MSC: 46B20 52A20 46B10 PDFBibTeX XMLCite \textit{A. R. Alimov}, East J. Approx. 2, No. 2, 215--232 (1996; Zbl 0866.46006)