[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2021.29.4.825

ON SENDOV'S CONJECTURE ABOUT CRITICAL POINTS OF A POLYNOMIAL

Nazir, Ishfaq (Department of Mathematics, University of Kashmir, South Campus)
Mir, Mohammad Ibrahim (Department of Mathematics, University of Kashmir, South Campus)
Wani, Irfan Ahmad (Department of Mathematics, University of Kashmir, South Campus)

Publication Information

Korean Journal of Mathematics / v.29, no.4, 2021 , pp. 825-831 More about this Journal

Abstract

The derivative of a polynomial p(z) of degree n, with respect to point α is defined by D_αp(z) = np(z) + (α - z)p'(z). Let p(z) be a polynomial having all its zeros in the unit disk |z| ≤ 1. The Sendov conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a zero of p'(z) within unit distance of each zero. In this paper, we obtain certain results concerning the location of the zeros of D_αp(z) with respect to a specific zero of p(z) and a stronger result than Sendov conjecture is obtained. Further, a result is obtained for zeros of higher derivatives of polynomials having multiple roots.

Keywords

polynomial; zeros; critical points; conjecture; polar derivative;

Citations & Related Records

Reference

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