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Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means

  • O. L. Vinogradov
  • V. V. Zhuk
Article

Some estimates for functionals indicated in the title are established. As implications, Jackson type inequalities with constants smaller than the previously known ones are obtained. The results hold in various spaces of both periodic and nonperiodic functions. Bibliography: 9 titles.

Keywords

General Estimate Type Inequality Moment Sequence Integrate Difference Jackson Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    V. V. Zhuk, “On V. A. Steklov funetions,” in: Differential Equations in Partial Derivatives {General Theory and Applications} [in Russian], St.Petersburg (1992), pp. 74–85.Google Scholar
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    O. L. Vinogradov and V. V. Zhuk, “An estimate for functionals in terms of powers of deviations of summator-integral operat0rs,” in: Approximation Theory (International Conference held in St.Petersburg on May 6–8, 2010), Abstracts (2010), pp. 9–10.Google Scholar
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    O. L. Vinogradov, “Sharp Jackson type inequalities for approximations of classes of convolutions by entier functions of finite degrees,” Algebra Analiz, 17, No. 4, 56–111 (2005).Google Scholar
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    V. V. Zhuk, Structural Properties of Functions and Approximation Accuracy [in Russian], Leningrad (1984).Google Scholar
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    O. L. Vinogradov and V. V. Zhuk, “The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus,” Zap. Nauchn. Semin. POMI, 383, 33–52 (2010).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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