Some Generalizations Involving the Polar Derivative for an Inequality of Paul Turán


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Authors: M. Y. MIR, S. L. WALI AND W. M. SHAH

DOI: 10.46793/KgJMat2606.1017M

Abstract:

For a polynomial P(z) := j=0najzj of degree n having all zeros in |z|≤ 1, It is known:

  ′     1     |an|− |a0|
|P (z)| ≥ 2 (n + |an|+|a0|)|P(z)|.

In this paper, besides the generalization of the above inequality, we extend some well-known results to the polar derivative of a polynomial.



Keywords:

Polynomials, inequalities, polar derivative, s-fold zeros.



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