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.
Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi, India.
Department of Mathematics, National Institute of Technology, Manipur, Imphal, India
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