Some refinements of Bernstein type inequalities for rational functions with zeros in a half plane

M. Y. Mir^a, G. M. Sofi^b, S. L. Wali^b, W. M. Shah<sup>b

a</sup> University of Kashmir, Kupwara Campus-190006, India
^b Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India

Abstract: Sofi and Shah proved some Bernstein-type inequalities for the class of rational functions $r(z)$ with all poles in a half-plane. In this paper, we consider all zeros of $r(z)$ to lie in the right half-plane and prove several refinements of these results, which, in turn, generalize some previously known results.

Keywords: polynomial, rational function, half plane, Bernstein-type inequality.

UDC: 517.53

MSC: 30A10, 30C10, 26D10

Received: 07.09.2025
Revised: 16.10.2025
Accepted: 17.10.2025

Language: English

DOI: 10.15393/j3.art.2025.19410