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Integral mean estimates for some operator preserving inequalities

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In this paper, some integral mean estimates for the polar derivative of a polynomial with complex coefficients are proved. We will see that these type of estimates are new in this direction and discuss their importance with respect to existing results comparatively. In addition, the obtained results provide valuable insights into the behavior of integrals involving operator preserving inequalities.

Abstract

In this paper, some integral mean estimates for the polar derivative of a polynomial with complex coefficients are proved. We will see that these type of estimates are new in this direction and discuss their importance with respect to existing results comparatively. In addition, the obtained results provide valuable insights into the behavior of integrals involving operator preserving inequalities.

참고문헌 (12)

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  7. N. K. Govil, "On Bernstein-type inequalities for the polar derivative of a polynomial", Progress in Approximation Theory and Applicable Complex Analysis, 117, pp.41~74 (2017)
  8. N. K. Govil, "On sharpening of an inequality of Turan", Appl. Anal. Discrete Math, 13(3), pp.711~720 (2019)[DOI]
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  10. M. Marden, "Geometry of polynomials" (1966), Mathematical Surveys, Amer. Math. Soc
  11. P. Turan, "Uber die Ableitung von Polynomen", Compos. Math, 7, pp.89~95 (1939)
  12. A. Zireh, "Inequalities for the polar derivative of a polynomial with restricted zeros", Kragjevac J. Math, 40(1), pp.113~124 (2016)[DOI]

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