Generalization of Zygmund type inequalities for the sth derivative of polynomials

Reingachan Ngamchui, Birkramjit Singh, Barchand Chanam

Abstract


If p(z) is a polynomial of degree n and p(z) ≠ 0 in |z| < 1, it was proved by Hans and Lal [Anal. Math. 40, 105-115(2014)] that for any β ∈ C with |β| ≤ 1,1 ≤ s ≤ n,

http://scik.org/public/site/images/bruce/eq_500_01

In this paper, we prove an inequality which gives an improved and generalized extension of the above inequality into Lγ norm.


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Published: 2021-06-29

How to Cite this Article:

Reingachan Ngamchui, Birkramjit Singh, Barchand Chanam, Generalization of Zygmund type inequalities for the sth derivative of polynomials, J. Math. Comput. Sci., 11 (2021), 5140-5155

Copyright © 2021 Reingachan Ngamchui, Birkramjit Singh, Barchand Chanam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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