HIGHER DERIVATIVE VERSIONS ON THEOREMS OF S. BERNSTEIN

Authors

  • Thangjam Birkramjit Singh Department of Mathematics, National Institute of Technology Manipur
  • Khangembam Babina Devi Department of Mathematics, National Institute of Technology Manipur
  • N. Reingachan Department of Mathematics, National Institute of Technology Manipur
  • Robinson Soraisam Department of Mathematics, National Institute of Technology Manipur
  • Barchand Chanam Department of Mathematics, National Institute of Technology Manipur

Abstract

In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

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Published

2022-05-26

Issue

Volume 27, Number 2, June 2022

Section

Articles