Certain estimates of the derivative of a meromorphic function on boundary of the unit disk

Abdullah Mir ()
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Abdullah Mir: University of Kashmir

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 749-760

Abstract: Abstract In this paper we establish a family of comparison inequalities between rational functions with prescribed poles for the sup-norms on the unit circle in the complex plane. Certain estimates for the modulus of the derivative of rational functions as well as some inequalities of Turán’s type are also obtained. The obtained results produce many inequalities for polynomials and polar derivatives as special cases.

Keywords: Rational functions; Bernstein inequality; poles; zeros; 30A10; 30C10; 26D10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0428-2

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