On Erdos – Lax and Turan Type Inequalities of a Polynomial

The above inequalities are respectively the well-known Erdӧs – Lax inequality and the Turẚn’s inequality.

A natural question that follows is to investigate the extension of these inequalities for open or closed disk of radius   In literature, we find extensions of Erdӧs – Lax inequality for a polynomial   of degree   having no zero in the open disk of radius   For   a similar extension does not seem to exist in general. In this paper, we discuss in brief why such an extension seems unattainable in general for   Further, we also give a brief account of the existence of extensions of Turẚn’s inequality for a polynomial   of degree   having all its zeros in the closed disk of radius  for every value of   in completion.

Author(S) Details

Kshetrimayum Krishnadas
Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi, India.

Barchand Chanam
Department of Mathematics, National Institute of Technology, Manipur, Imphal, India

View Book:- https://stm.bookpi.org/NRAMCS-V3/article/view/6812

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