The best quadrature formula of markov type for classes functions, which given by modulus of continuity

Authors

  • Mirgand Sh. Shabozov Institute of Mathematics of the Academy of Sciences of the Republic of Tajikistan, Aini st., 299, Dushanbe, 734063, Tajikistan;
  • Adolat A. Shabozova Tajik State National University, Rudaki pr., 17, Dushanbe, 734025, Tajikistan;

Abstract

In this paper for the classes of functions which given by modulus of continuity is solved finding the extremal problem of the best quadrature formula of Markov type. It is proved that the optimal formula is classical quadrature formula of trapezium and calculated it’s exact estimate of error on the given classes function. Analogous fact is proved for the classes function given by modulus smoothness and also for intermediate interval classes function between the above mentioned classes functions given by modulus of continuity and modulus of smoothness. Refs 10.

Keywords:

quadrature formula of Markov type, modulus of continuity, error

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Published

2014-02-01

How to Cite

Shabozov, M. S., & Shabozova, A. A. (2014). The best quadrature formula of markov type for classes functions, which given by modulus of continuity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(1), 79–86. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11030

Issue

Vol. 1 No. 1 (2014)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.