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Abstract and Applied Analysis
Volume 2009 (2009), Article ID 165194, 19 pages
http://dx.doi.org/10.1155/2009/165194
Review Article

S. N. Bernstein Type Estimations in the Mean on the Curves in a Complex Plane

Institute of Mathematics and Mechanics, Baku State University, 370148 Baku, Azerbaijan

Received 3 June 2009; Accepted 3 August 2009

Academic Editor: John Rassias

Copyright © 2009 J. I. Mamedkhanov and I. B. Dadashova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. N. Mergelian, “Some questions of the constructive theory of functions,” Proceedings of the Steklov Institute of Mathematics, vol. 37, pp. 3–90, 1951 (Russian). View at Google Scholar
  2. N. A. Lebedev and P. M. Tamrazov, “Inverse approximation theorems on regular compacta of the complex plane,” Mathematics of the USSR-Izvestiya, vol. 34, no. 6, pp. 1340–1390, 1970 (Russian). View at Google Scholar · View at MathSciNet
  3. V. K. Dzjadyk, Introduction to the Theory of Approximation of Functions by Polynomials, Nauka, Moscow, Russia, 1977.
  4. J. I. Mamedkhanov and I. B. Dadashova, “Singular characteristics in S.N. Bernstein classic estimations,” in Modern Problems of Mathematics and Related Questions, pp. 148–152, Scientific Centre of the Russian Academy of Sciences, Dagestan State Tekhnical University, Makhachkala, Russia, 2008. View at Google Scholar
  5. V. V. Salayev, “Primal and inverse estimations for Cauchy's singular integral on a closed curve,” Matematicheskie Zametki, vol. 19, pp. 365–380, 1976 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. V. Andrievskii, “Geometric properties of V. K. Dzyadyk domains,” Ukrainian Mathematical Journal, vol. 33, no. 6, pp. 723–727, 1980 (Russian). View at Google Scholar · View at MathSciNet
  7. V. I. Belyi, “Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary,” Matematicheskii Sbornik, vol. 102(144), no. 3, pp. 331–361, 1977 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. I. Mamedhanov, “Estimates of the derivatives of analytic functions on curves,” Doklady Akademii Nauk SSSR, vol. 217, no. 3, pp. 526–528, 1974 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. I. Mamedkhanov, “Markov-Bernstein inequalities on V.V.Salayev's curves,” in Theory of Functions and Approximations, Proceedings of the Second Saratov Winter School, Saratov, Russia, 1986. View at Google Scholar
  10. J. I. Mamedkhanov, “Some integral inequalities for polynomials on the curves in complex domain,” in Special Questions of Theory of Functions, Baku, Azerbaijani, 1989. View at Google Scholar
  11. M. I. Andrashko, “Inequalities for a derivative of algebraic polynomial in the metric Lp, (p1) in domains with angles,” Ukrainian Mathematical Journal, vol. 16, no. 4, pp. 439–444, 1964 (Russian). View at Google Scholar
  12. V. I. Belyi, Methods of conformal invariants in theory of approximation of functions of a complex variable, Ph.D. thesis, Kiev, Ukraine, 1978.
  13. V. V. Andrievskii, “On pproximation of functions by partial sums of a series in Faber polynomials on continua with a nonzero local geometric characteristic,” Ukrainian Mathematical Journal, vol. 32, no. 1, pp. 3–10, 1980 (Russian). View at Google Scholar · View at MathSciNet
  14. V. V. Andrievskii, “Some properties of continua with a piecewise quasiconformal boundary,” Ukrainian Mathematical Journal, vol. 32, no. 4, pp. 435–440, 1980 (Russian). View at Google Scholar · View at MathSciNet
  15. E. P. Dolzhenko and V. I. Danchenko, “Mapping of sets of finite α-measure by means of rational functions,” Mathematics of the USSR-Izvestiya, vol. 51, no. 6, pp. 1309–1321, 1987 (Russian). View at Google Scholar · View at MathSciNet