Certain Inequalities for the generalized polar derivative of a polynomial

2025/10/03 by N. A. Rathe, Rathe, N. A., D. R. Bhat +3
Mathematics · #26D05 #26D10 #30A10 #41A17 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2510.02775

openalex publication_date 2025/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Rather et al. \citeNT considered the generalized derivative and the generalized polar derivative and studied the relative position of zeros of generalized derivative and generalized polar derivative with respect to the zeros of polynomial. \indent In this paper, we establish some inequalities that estimate the maximum modulus of generalized derivative and the generalized polar derivative of the polynomial P(z), which is also the extension of recently known results.

Citations

• Inequalities for the Polar Derivative of a Polynomial
• On an inequality concerning the polar derivative of a polynomial
• Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros

Related

• Inequalities for the Polar Derivative of a Polynomial
• Generalizations of Some Inequalities of the Polar Derivatives of Polynomials
• A Note On Generalized L_p Inequalities for the polar derivative of a polynomial
• Some Inequalities for the Polar Derivative of Some Classes of Polynomials
• Zygmund's type inequality to the polar derivative of a polynomial