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Bernstein-type inequalities preserved by modified Smirnov operator
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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.
Abstract
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.
참고문헌 (9)
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- S. N. Bernstein, "Sur l’ordre de la meilleure approximation des fonctions continues par des polynˆomes de degre´ donn´e", Memoires de l’Academie Royals de Belgique, 4, pp.1~103 (1912)
- S. Bernstein, "Sur la limitation des derivees des polynomes", C. R. Acad. Sci. Paris, 190, pp.338~340 (1930)
- E. G. Ganenkova, "The M¨obius Transformation and Smirnov’s Inequality for Polynomials", Mathematical Notes, 2, pp.216~226 (2019)
- E. G. Ganenkova, "Variations on a theme of the Marden and Smirnov operators, differential inequalities for polynomials", J. Math. Anal. Appl, 476, pp.696~714 (2019)
- E. Kompaneets, "Generalization of Smirnov Operator and Differential inequalities for polynomials", Lobachevskii Journal of Mathematics, 40, pp.2043~2051 (2019)
- P. D. Lax, "Proof of a conjecture of P. Erdo¨s on the derivative of a polynomial", Bull. Amer. Math. Soc, 50, pp.509~513 (1944)
- V. I. Smirnov, "Constructive theory of functions of a complex variable" (1964), Nauka
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