Korean Journal of Mathematics

  • 제30권2호
  • /
  • Pages.305-313
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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BERNSTEIN-TYPE INEQUALITIES PRESERVED BY MODIFIED SMIRNOV OPERATOR

  • 투고 : 2021.11.11
  • 심사 : 2022.06.25
  • 발행 : 2022.06.30
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초록

In this paper we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some results which in turn provide the compact generalizations of some well-known inequalities for polynomials.

키워드

과제정보

The authors are highly grateful to the refree for his/her useful suggestions.

참고문헌

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  3. S. N. Bernstein, Sur l'ordre de la meilleure approximation des fonctions continues par des polynomes de degre donne, Memoires de l'Academie Royals de Belgique 4 (1912), 1-103.
  4. S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad. Sci. Paris. 190 (1930), 338-340.
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  7. E. Kompaneets and V. Starkov, Generalization of Smirnov Operator and Differential inequalities for polynomials, Lobachevskii Journal of Mathematics, 40, (2019), 2043-2051. https://doi.org/10.1134/s1995080219120047
  8. P. D. Lax, Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509-513. https://doi.org/10.1090/S0002-9904-1944-08177-9
  9. V. I. Smirnov and N. A. Lebedev, Constructive theory of functions of a complex variable, (Nauka, Moscow,1964) [Russian].