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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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kshetrimayum Krishnadas & Reingachan Ngamchui & Barchand Chanam, 2021. "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," Mathematics, MDPI, vol. 9(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:887-:d:537569
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