MATHEMATICS

Inequalities for the derivative of rational functions with prescribed poles and restricted zeros

U. M. Ahanger, W. M. Shah

Central University of Kashmir, Ganderbal J & K, 191201, India

Abstract: In this paper, instead of assuming that a rational function $r(z)$ with prescribed poles has a zero of order $s$ at origin, we suppose that it has a zero of multiplicity s at any point inside the unit circle, whereas the remaining zeros are within or outside a circle of radius $k$ and prove some results which besides generalizing some inequalities for rational functions include refinements of some polynomial inequalities as special cases.

Keywords: inequalities, polynomials, rational functions, poles, zeros.

UDC: 517.537

MSC: 30A10, 30C10, 30C15

Received: 23.09.2022
Accepted: 16.02.2023

DOI: 10.21638/spbu01.2023.309