10.57647/cna.2025.qc6k-e772

On Erdos-Lax Inequality for the Class of Composite Polynomials

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  • Bashir Ahmad Ganie*1,
  • Varun Mohan1,
  • Khursheed Alam1,
  1. Department of Mathematics, Sharda University Gr Noida UP, 201310, India

Received: 2024-10-11

Revised: 2024-12-22

Accepted: 2025-02-13

Published in Issue 2025-06-30

Copyright (c) 2025 Bashir Ahmad Ganie, Varun Mohan, Khursheed Alam, Department of Mathematics, Government Degree College Drass, Kargil, 194102, India (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On Erdos-Lax Inequality for the Class of Composite Polynomials. (2025). Communications in Nonlinear Analysis, 13(1), 16-20. https://doi.org/10.57647/cna.2025.qc6k-e772

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Abstract

Let  $P(z)= \sum_{j=0}^{n}a_{j}{z}^{j}\in \mathcal{P}_{n}$, and $P(z)$ not vanishing in $|z|<1$. Kumar (CRM, 360, 2022, 1081-1085) proved that if $P(z) =\sum_{j=0}^{n}a_{j}{z}^{j}$ such that $P(z) \ne 0$ in $|z|<1$, then
$$\max_{z\in T_1}|P^\prime(z)|\leq \frac{n}{2}\left\{1- \frac{|a_{0}|-|a_{n}|}{n(|a_{0}|+|a_{n}|)}\right\} \max_{z\in T_1}|P(z)|$$
In this paper, we present a generalization of this inequality by considering a more general class of polynomials $P(Q(z))$ of degree $mn$, with $Q(z)$ being a polynomial of degree $m$. The obtained result, besides yielding some interesting results as corollaries, includes some known results as special cases.

Keywords

  • Inequalities,
  • Derivative,
  • Polynomial,
  • Zeros
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