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On an operator preserving polynomial inequalities

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In this paper, we consider an operator $N : \mathcal{P}_n\rightarrow \mathcal{P}_n$ on the space of polynomials $\mathcal{P}_n$ of degree at most $n$ and establish some compact generalizations of Bernstein-type polynomial inequalities, which include several well known polynomial inequalities as special cases.

Abstract

In this paper, we consider an operator $N : \mathcal{P}_n\rightarrow \mathcal{P}_n$ on the space of polynomials $\mathcal{P}_n$ of degree at most $n$ and establish some compact generalizations of Bernstein-type polynomial inequalities, which include several well known polynomial inequalities as special cases.

참고문헌 (15)

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  4. S. N. Bernstein, "On the best approximation of continuous functions by polynomials of given degree (O nailuchshem problizhenii nepreryvnykh funktsii posredstrvom mnogochlenov dannoi stepeni)", Sobraniye sochinenii, 1, pp.11~104 (1952)
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  11. G. Polya, "Aufgaben und lehrsatze aus der Analysis" (1925), Springer-Verlag
  12. N. A. Rather, "On the zeros of certain composite polynomials and an operator preserving inequalities", The Ramanujan Journal[DOI]
  13. H. Queffelec, "Diophantine approximation and Dirichlet series" (2013)
  14. Q. I. Rahman, "Analytic Theory of Polynomials", pp.243~270 (2002), Clarendon Press Oxford
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