On the zeros of polynomials and their generalized derivative

Articles in Press

Document Type : Research Paper

Authors
Mohammad Ibrahim Mir
Shahadat Ali
Jamina Banoo
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
10.22075/ijnaa.2024.35648.5300
Abstract
In this paper, we present findings on the placement of zeros of generalized derivative of polynomials, drawing parallels to those observed in the ordinary derivative of polynomials. Mathematicians have broadened the scope of the Gauss-Lucas Theorem, a classic principle that deals with zero location in polynomials and their derivatives. The new work expands it to cover convex linear combinations of incomplete polynomials.
Keywords
Polynomials
Half-plane
Specht Theorem
Gauss-Lucas Theorem
Generalized Derivative
Grace Heawood Theorem
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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 26 August 2025

  • Receive Date 17 October 2024
  • Accept Date 27 November 2024