**The exact constant in a weak-type inequality for polynomials,**in Internat. Conf. on the Theory of Approximation of Functions, USSR, Kiev, May 30 - June 6, 1983, Abstracts of papers, Ukrain. Akad. Nauk SSR, Inst. Mat., Kiev, 1983, page 11. In Russian.**The exact constant in a weak-type inequality for polynomials,**Proc. Internat. Conf. on the Theory of Approximation of Functions, USSR, Kiev, May 30 - June 6, 1983, Nauka, Moscow, 1987, pp. 25-26. Bibliogr.: 2 ref. In Russian.**An extremal problem for polynomials,**Mat. Zametki. 35 (1984), no. 3, pp. 349-356; English translation: Math. Notes 35 (1984), no. 3-4, pp. 181-186. Bibliogr.: 6 ref. (Math. Rev. 85i:42001).**An extremal problem for polynomials with a fixed mean value,**in Approximation of Functions by Polynomials and Splines, ed. Yu. N. Subbotin, Akad. Nauk SSSR, Ural. Tsentr, Sverdlovsk, 1985, pp. 15-22, 149. Bibliogr.: 4 ref. In Russian. (Math. Rev. 87j:42002).**A property of the unit ball of an infinite-dimensional linear normed space,**in Approximation of Functions by Polynomials and Splines, ed. Yu. N. Subbotin, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk, 1985, pp. 23-24, 149. Bibliogr.: 3 ref. In Russian. (Math. Rev. 87i:41030).**An extremal problem for nonnegative trigonometric polynomials,**in Theory of Functions and Approximations, Part 2, Proc. of the Second Saratov Winter School held in Saratov, January 24 - February 5, 1984, ed. S.M. Nikol'skii, Saratov. Gos. Univ., Saratov, 1986, pp. 32-34. Bibliogr.: 2 ref. (Math. Rev. see 89j:00036).**Discrete Jackson inequality in a Hilbert space of periodic functions given on uniform grid,**in Conference of Young Mathematicians (Sverdlovsk, January 13-17, 1986), Information Materials, Preprint, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk, 1986, pp. 8-9. Bibliogr.: 2 ref. In Russian.**The exact constant in the Jackson inequality in**Mat. Zametki 39 (1986), no. 5, pp. 651-664; English translation: Math. Notes 39 (1986), no. 5-6, pp. 355-363. Bibliogr.: 11 ref. (Math. Rev. 87j:42003).*L*^{2},**Discrete analog of the Jackson inequality in**Akad. Nauk SSSR, Ural. Nauchn. Tsentr IMM, Sverdlovsk, 1986, 38 pages. Bibliogr.: 23 ref. The Manuscript is deposited in VINITI 11.05.86. N 3369-B86. In Russian.*L*^{2},**The Jackson inequality in a space of square-summable functions,**in Theory of Functions and Approximations, Part 1, Proc. of the Third Saratov Winter School held in Saratov, January 27 - February 7, 1986, ed. S.M. Nikol'skii, Saratov. Gos. Univ., Saratov, 1987, pp. 134-136. Bibliogr.: 5 ref. In Russian. (Math. Rev. see 90j:00006).**(Coauthors: S.V. Konyagin and I.G. Csar'kov)**in Differential Equations, Harmonic Analysis and Their Applications, ed. O.A. Oleinik, V.A. Sadovnichii, P.L. Ul'yanov, Moscow Univ., Moscow, 1987, pp. 59-62. Bibliogr.: 4 ref. In Russian.

An approximation of solution of the equation*f*(*x*) =*x*,**A Jackson inequality in the space**Approximation in Concrete and Abstract Banach Spaces, ed. Yu. N. Subbotin, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk, 1987, pp. 4-14, 123. Bibliogr.: 11 ref. In Russian. (Math. Rev. 89f:41020).*L*^{2},**Extremal properties of polynomials and exact estimations of mean-square approximations,**Avtoreferat Dis. Kand. Fiz.-Mat. Nauk: 01.01.01.- Mat. Analiz, Nadzag., UrGU, Sverdlovsk, 1987, 16 pages. Bibliogr.: 25 ref. In Russian.**The exact constant in the Jackson inequality in**Trudy Mat. Inst. im. V.A. Steklova 180 (1987), pp. 32-33; English translation: Proc. of the Steklov Inst. of Math. 180 (1987). Bibliogr.: 7 ref.*L*^{2}in case of small argument of the modulus of continuity,**A Jackson inequality for mean-square approximations of periodic functions by trigonometric polynomials on a uniform net,**Mat. Zametki 43 (1988), no. 4, pp. 460-473; English translation: Math. Notes 43 (1988), no. 3-4, pp. 264-272. Bibliogr.: 15 ref. (Math. Rev. 89h:42004).**Extremal properties of non-negative trigonometric polynomials and Jackson inequality in**in Extremal Problems of the Approximation Theory and Their Applications, Abstracts of Communications of Republican Scientific Conference, Kiev, May 29-31, 1990, ed. N.P. Korneichuk, Inst. Mat. Akad. Nauk USSSR, Kiev, page 12. Bibliogr.: 3 ref. In Russian.*L*^{2},**Weak-type inequalities for trigonometric polynomials,**Proc. of the Institute of Mathematics and Mechanics, Vol. 2, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 1992, pp. 34-41, 225. Bibliogr.: 4 ref. In Russian. (Math. Rev. 95k:42001).**A best approximation of a class**in Youth Conf. "Problems of Theoretical and Applied Mathematics ", Abstracts of Communications of Conferences N 22-24 held in 1991-1993 years, ed. V.I. Berdyshev, RAN. UrO. IMM, Ekaterinburg, 1993, page 94. Bibliogr.: 2 ref. In Russian.*W*^{r}_{2}by trigonometric polynomials in*C*,**The Jackson inequality in**in Theory of Functions and Approximations, Part 1, Proc. of the Seventh Saratov Winter School held in Saratov, January 30 - February 4, 1994 (Memory of the Professor A.A. Privalov), ed. S.M. Nikol'skii, Saratov. Gos. Univ., Saratov, 1995, pp. 104-108. Bibliogr.: 8 ref. In Russian.*L*^{2}on sphere,**Exact Jackson inequality in space**in The Algorithmic and Numerical Analysis of the Ill-posed Problems, Abstracts of Communications of the All-Russia Scientific Conference Dedicated to the Memory V.K. Ivanov, February 27 - March 3, Ekaterinburg, 1995, ed. V.V. Vasin, UrGU, IMM UrO RAN, Ekaterinburg, 1995, pp. 25-26. Bibliogr.: 5 ref. In Russian.*L*^{2}with Laguerre weight,**Sharp Jackson-Stechkin inequality in**Mat. Zametki 60 (1996), no. 3, pp. 333-355; English translation: Math. Notes. 60 (1996), no. 3, pp. 248-263. Bibliogr.: 42 ref.*L*^{2}for functions on multidimensional spheres,**The exact Jackson inequality in the space**in Materials of the International Conference and Chebyshev Readings, Dedicated to the to P.L. Chebyshev 175 Anniversary, Vol. 1, Mech. and Math. Dep. of Moscow State University, Moscow, 1996, pp. 40-43. Bibliogr.: 7 ref. In Russian.*L*^{2}with Jacobi weight,**(Coauthor: V.V. Arestov)**Trudy Mat. Inst. im. V.A. Steklova 219 (1997), pp. 44-73; English translation: Proc. of the Steklov Inst. of Math. 219 (1997), pp. 36-65. Bibliogr.: 21 ref.

On Delsarte scheme of estimating the contact numbers,**Jackson-Stechkin constant in**V Jornadas Zaragoza-Pau de Matematica Aplicada y Estadistica, Jaca 15-16 de Septiembre de 1997. Conf. Resum. Particpantes. Zaragoza-Pau, 1997, page 14. Bibliogr.: 4 ref. (In English).*L*^{2}on the segment with Jacobi weight, on the sphere and projective spaces,**(Coauthor: V.V. Arestov)**in Modern Problems of the Theory of Functions and Their Applications, Abstracts of Communications of the Ninth Saratov Winter School held in Saratov, January 26 - February 1, 1998, Saratov. Gos. Univ., Saratov, 1997, page 14. In Russian.

An extremal problem connected with upper estimating the contact numbers of Euclidean spaces,**(Coauthor: V.V. Arestov)**Izvestiya of the Tula State University. Ser. Mathematics. Mechanics. Informatics. Tula State University, Tula, 4 (1998), no. 1, pp. 36-39, 162-163. Bibliogr.: 11 ref. In Russian.

Some properties of solutions of Delsarte type problem and its dual problem,**(Coauthor: V.V. Arestov)**in Geometric Aspects of Fourier and Functional Analysis (Kiel, August 10-14, 1998), Mathematisches Seminar Christian-Albrechts-University of Kiel, Germany, 1998, page 1.

Properties of solutions of Delsarte type problem and its dual problem,**Sharp Jackson-Stechkin inequality in**Izv. Ross. Akad. Nauk, Ser. Mat., 62 (1998), no. 6, pp. 27-52.; English translation: Izvestiya: Mathematics, 62:6 (1998), pp. 1095-1119. Bibliogr.: 49 ref.*L*^{2}on the segment with Jacobi weight and projective spaces,**(Coauthors: N.I. Chernykh and V.T. Shevaldin)**in The Algorithmic and Numerical Analysis of the Ill-posed Problems, Abstracts of Communications of the All-Russia Scientific Conference Dedicated to the Memory V.K. Ivanov, (Ekaterinburg, February 2-3, 1998), ed. V.V. Vasin, UrGU, Ekaterinburg, 1998, pp. 41-42. Bibliogr.: 3 ref. In Russian.

Estimation of approximation of periodic function by trigonometric polynomials by means of it the trigonometric modulus of continuity in space*L*^{2},**Sharp Jackson-Stechkin inequality in**in Abstracts of Communications of Internat. Conf. "Approximation Theory and Harmonic Analysis", Tula, Russia, May 26-29,1998, Tula State University, Tula, 1998, pp. 26-28. In Russian.*L*^{2}(*R*^{m}) with spherical modulus of continuity,**Sharp Jackson-Stechkin inequality in the space**Proc. of the Institute of Mathematics and Mechanics, Vol. 5, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 1998, pp. 183-198, 333. Bibliogr.: 30 ref. In Russian.*L*^{2}(*R*^{m}),**(Coauthor: V.V. Arestov)**The Bulletin of Association of Mathematical Programming. Scientific Edition, ed. L.D. Popov, UrO RAN, Ekaterinburg, No. 8, 1999, pp. 25-26. Bibliogr.: 3 ref. In Russian.

Solution of an inverse Delsarte problem,**(Coauthor: V.V. Arestov)**in Abstracts of Communications of the Workshop "Modern Methods of the Theory of Functions and Adjacent Problems", Voronezh, Russia, January 27 - February 4, 1999, Voronezh Gos. Univ., Voronezh, 1999, page 18. Bibliogr.: 1 ref. In Russian.

On the minimum distance of spherical codes cardinality of 24 and 25 in*R*^{4},**(Coauthors: N.I. Chernykh and V.T. Shevaldin)**Mat. Zametki, 65 (1999), no. 6, pp. 928-932; English translation: Math. Notes. 65 (1999), no. 6, pp. 777-781. Bibliogr.: 4 ref.

Jackson-Stechkin inequality in*L*^{2}with trigonometric modulus of continuity,**(Coauthor: V.V. Arestov)**

On Kissing Number in Four Dimensions,

(PS format),

(PDF format),

in Research Communications of the conference held in the memory of Paul Erdös, Budapest, Hungary, July 4-11, 1999, ed. A. Sali, M. Simonovits and V.T. Sos, Janos Bolyai Math. Soc., Budapest, 1999, pp. 10-14. Bibliogr.: 11 ref.**Sharp Jackson-Stechkin inequality for mean-quadratic approximation on some classical manifolds,**Resumes, Fourth International Conference "Curves and Surfaces", Saint-Malo, France, July 1-7, 1999, Association Francaize d'Approximation, 1999, pp. 3-4. Bibliogr.: 6 ref.**Jackson-Stechkin constant in**in Actas de las V Jornadas Zaragoza-Pau de Matematica Aplicada y Estadistica, ed. Monique Madaue-Tort, Maria Cruz Lopez De Silanes, Gerardo Sanz and Miguel San Miguel, Publicaciones del Seminario Matematico GARCIA DE GALDEANO, Universidad de Zaragoza, Zaragoza, 1999, pp. 109-116. Bibliogr.: 18 ref.*L*^{2}on the segment with Jacobi weight, on the sphere and projective spaces,**(Coauthor: V.V. Arestov)**Workshop on Theory of Functions "Ozersk-99", April 16-19, 1999, Abstracts of Communications, OTI MIFI, Ozersk, 1999, pp. 11-15. Bibliogr.: 13 ref. In Russian.

On arrangements of 25 and 24 points on unit sphere of Euclidean four-dimensional space,**(Coauthors: V.V. Arestov and M.V. Deikalova)**Workshop on Theory of Functions "Ozersk-99", April 16-19, 1999, Abstracts of Communications, OTI MIFI, Ozersk, 1999, pp. 16-20. Bibliogr.: 3 ref. In Russian.

On Delsarte problem on the segment [-1,1/3] for ultraspherical polynomials,**(Coauthors: V.V. Arestov and M.V. Deikalova)**in Proceedings of the S.B. Stechkin's International Workshop on Theory of Functions (Miass of Chelyabinsk Province, Russia, July 24 - August 3, 1998), Ural Branch of Russian Academy of Sciences, Inst. of Math. and Mech., Ekaterinburg, 1999, pp. 5-37. Bibliogr.: 18 ref. In Russian.

Delsarte type problem connected with 1/3-spherical code in Euclidean space of dimension 4, 5, 6,**Sharp Jackson-Stechkin inequality for**in Proceedings of the S.B. Stechkin's International Workshop on Theory of Functions (Miass of Chelyabinsk Province, Russia, July 24 - August 3, 1998), Ural Branch of Russian Academy of Sciences, Inst. of Math. and Mech., Ekaterinburg, 2000, pp. 38-63. Bibliogr.: 33 ref. (In Russian).*L*^{2}-approximations on the half-line with Laguerre weight,**(Coauthors: N.I. Chernykh and V.T. Shevaldin)**in Modern Problems of the Theory of Functions and Their Applications, Abstracts of Communications of the 10th Saratov Winter School held in Saratov, January 27 - February 2, 2000, Saratov. Gos. Univ., Saratov, 2000, pp. 12-13. In Russian.

Jackson-Stechkin inequality in*L*^{2}with modulus of continuity generated by differential operator,**(Coauthors: N.I. Chernykh and V.T. Shevaldin)**in Theory of approximation of functions and operators, Abstracts of Communications of the International Conference dedicated to the 80th birthday of S.B.Stechkin (Russia, Ekaterinburg, February 28 - March 3, 2000), Ural. Gos. Univ., Ekaterinburg, 2000, pp. 18-20. Bibliogr.: 1 ref. In Russian.

Estimates of exact constant in Jackson-Stechkin inequality in*L*^{2},**(Coauthor: V.V. Arestov)**Mat. Zametki, 68 (2000), no. 4, pp. 483-503; English translation: Math. Notes. 68 (2000), no. 4, pp. 419-435. Bibliogr.: 24 ref.

Estimates of maximal value of angular code distance for 24 and 25 points on unit sphere in^{4},**On minimal Jackson-Stechkin constant in**in Abstracts of the Internat. Conf.: Achievement and Development of Mathematics in Framework of Program "Kazakhstan in Third Millennium" (Almaty, Oct. 26-28, 2000), Institute of Mathematics, Almaty, 2000, page 63. Bibliogr.: 3 ref. In Russian.*L*^{2},**(Coauthors: V.V. Arestov and M.V. Deikalova ) Delsarte problem connected with spherical 1/3-code,**Approximation Theory and its Applications, Proc. of the Institute of Mathematics of NAS of Ukraine, v. 31, 2000, pp. 33-48.**About an interval of the constancy of the minimal Jackson-Stechkin constant in**in Abstracts of Communications of the Workshop "Modern Methods of the Theory of Functions and Adjacent Problems", Voronezh, Russia, January 27 - February 4, 2001, Voronezh Gos. Univ., Voronezh, 2001, pp. 23-24. In Russian.*L*^{2},**Estimations of optimal point of minimal Jackson constant in space**in Abstracts of Communications of the All-Russia Conference "Algorithmical Analysis of Instable Problems" Russia, Ekaterinburg, February 26 - March 2, 2001, Ural. Gos. Univ., Ekaterinburg, 2001, pp. 12-13. Bibliogr.: 4 ref. In Russian.*L*^{p}for 1*p*2,**Minimal Jackson-Stechkin constant in**in Proceeding of the Internat. Conf.: Achievement and Development of Mathematics in Framework of Program "Kazakhstan in Third Millennium" (Almaty, October 26-28, 2000), Institute of Mathematics, Almaty, 2001, pp. 72-76. Bibliogr.: 6 ref. In Russian.*L*^{2},**Universal lower bound for Jackson-Stechkin constant in**// Theory of Approximations and Harmonic Analysis. Abstracts of Reports. Collection of Abstracts of Reports of Participants of 10th Section of Ukrainian Congress of Mathematics devoted to the 200th anniversary of the birth of M. V. Ostrohrads'ky (Kyiv, Ukraine, August 21-23, 2001), Institute of Mathematics of the Ukrainian National Academy of Sciences, Kyiv, 2001, pp. 5-6. Bibliogr.: 2 ref.*L*^{2}**On the Jackson-Stechkin inequality for the best**// Proceedings of the Steklov Institute of Mathematics, Suppl. 1, 2001, pp. S30-S47. Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 7, No. 1, 2001. Bibliogr.: 66 ref.*L*^{2}-approximations of functions by trigonometric polynomials**Jackson-Stechkin inequality and related extremal problems,**in Abstracts of Conference "Functional Methods in Approximation Theory, Operator Theory, Stochastic Analysis and Statistics" (Kyiv, Ukraine, October 19-22, 2001), Taras Shevchenko National University of Kyiv, Kyiv, 2001, p. 3.**Direct theorems of approximation theory, exact constants and related extremal problems,**in Modern Problems of the Theory of Functions and Their Applications, Abstracts of Communications of the 11th Saratov Winter School held in Saratov in memory of the famous Professors N.K.Bari and D.E.Men'shov from Moscow State University, January 28 - February 4, 2002, Saratov. Gos. Univ., Saratov, 2002. To appear. In Russian.**(Coauthor: V.V. Arestov)**// Approximation Theory: A volume dedicated to Blagovest Sendov. Submitted in 2001. Bibliogr.: 15 ref.

Continuity of the Best Constant in the Jackson Inequality in*L*^{2}with respect to Argument of Modulus of Continuity