Generalized and Extended Versions of Ankeny–Rivlin and Improved, Generalized, and Extended Versions of Rivlin Type Inequalities for the s th Derivative of a Polynomial

Kshetrimayum Krishnadas, Reingachan Ngamchui and Barchand Chanam
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Kshetrimayum Krishnadas: Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, Phase II, Sheikh Sarai, New Delhi 110017, Delhi, India
Reingachan Ngamchui: Department of Mathematics, National Institute of Technology Manipur, Imphal 795004, Manipur, India
Barchand Chanam: Department of Mathematics, National Institute of Technology Manipur, Imphal 795004, Manipur, India

Mathematics, 2021, vol. 9, issue 8, 1-18

Abstract: Let p ( z ) be a polynomial of degree n having no zeros in | z | < 1 . In this paper, we generalize and extend a well-known result proven by Ankeny and Rivlin for the s t h derivative of the polynomial. Furthermore, another well-known result proven by Rivlin is also improved, generalized and extended for the s t h derivative of p ( z ) . Our results also give a number of interesting consequences as special cases.

Keywords: s th derivative; polynomial; maximum modulus; zeros (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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