Estimates for the polar derivative of a constrained polynomial on a disk




This work is a part of a recent wave of studies on inequalities which relate the uniform-norm of a univariate complex coefficient polynomial to its derivative on the unit disk in the plane. When there is a limit on the zeros of a polynomial, we develop some additional inequalities that relate the uniform-norm of the polynomial to its polar derivative. The obtained results support some recently established ErdÅ‘s-Lax and Turán-type inequalities for constrained polynomials, as well as produce a number of inequalities that are sharper than those previously known in a very large literature on this subject.


Complex domain , Constrained polynomial , Rouché‘s theorem , Zeros
  • Pages: 541–554
  • Date Published: 2022-12-21
  • Vol. 24 No. 3 (2022)

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How to Cite

G. V. Milovanović, A. Mir, and A. Hussain, “Estimates for the polar derivative of a constrained polynomial on a disk”, CUBO, vol. 24, no. 3, pp. 541–554, Dec. 2022.