ON A LOWER BOUND INEQUALITY FOR THE DERIVATIVE OF A POLYNOMIAL


By

Susheel Kumar1 , Roshan Lal2 and Pradumn Kumar3

1Department of Mathematics, Deshbandhu College University of Delhi, Kalkaji-110019, New Delhi, India

2V.S.K.C. Government Postgraduate College, Dakpathar, Dehradun-248125, Uttarakhand, India

3Department of Physics, Hindu College (University of Delhi), Delhi-110007, India

Email:skahlawatt@gmail.com, rlkeshtwal@gmail.com, drpradumnkumar@rediffmail.com

(Received : October 26, 2021 ; In format : November 20, 2021; In final form : March 04, 2022)


Abstract

Let P(z) be a polynomial of degree n having all its zeros in |z| < K, K > 0 while s-fold zeros are located at origin. In this paper, by motivation with a result of Aziz[A Refinement of an Inequality of S. Bernstein, Journal of Mathematical Analysis and Applications, 144 (1989), 226-235.], we propose some new estimates of the lower bound of |P' (z)| in terms of max |P(z)| on |z| = 1. 2020


Mathematical Sciences Classification: 30D15, 30A10.

Keywords and Phrases: Polynomials; Inequalities; maximum modulus; Zeros.



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