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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