On the Derivative of a Polynomial with Prescribed Zeros

Journal Title: Journal of Mathematics and Applications - Year 2017, Vol 40, Issue

Abstract

For a polynomial [formula] of degree n having all its zeros in |z| ≤ K, K ≥ 1it is known that [formula]. By assuming a possible zero of order m, 0 ≤m ≤ n – 4, at z=0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.

Authors and Affiliations

Vinay K. Jain

Keywords

Related Articles

A Refinement of Schwarz’s Lemma and its Applications

By using the value of the second derivative of the function at 0, along with the values of the function and its first derivative at 0, we have obtained a refinement of well known Schwarz’s lemma and have used this refine...

The Real and Complex Convexity

We prove that the holomorphic differential equation [formula] (φ: C → C be a holomorphic function and (γ,c) ∈ C^2) plays a classical role on many problems of real and complex convexity. The condition exactly [formula] (i...

Number of Zeros of a Polynomial (Lacunary-type) in a Disk

The problem of finding out the region which contains all or a prescribed number of zeros of a polynomial P(z) := [formula] has a long history and dates back to the earliest days when the geometrical representation of com...

On the Evolution of Academic Staff Structure in a University Setting

This paper models the academic staff structure in a university as a system of stocks and flows in a three-dimensional space, ℝ3. The stocks are the number of academic staff in a particular state at a given time and the f...

On differential sandwich theorems of analytic functions defined by certain generalized linear operator

In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Som...

Download PDF file
  • EP ID EP342922
  • DOI 10.7862/rf.2017.7
  • Views 58
  • Downloads 0

How To Cite

Vinay K. Jain (2017). On the Derivative of a Polynomial with Prescribed Zeros. Journal of Mathematics and Applications, 40(), 97-120. https://europub.co.uk/articles/-A-342922