$L^{\gamma}$ INEQUALITIES
CONCERNING POLYNOMIALS
Kshetrimayum Krishnadas1, Barchand Chanam2
1Shaheed Bhagat Singh College (University of Delhi)
Sheikh Sarai Phase II
New Delhi - 110017, INDIA
2 National Institute of Technology Manipur
Langol, Imphal - 795004, INDIA

Abstract

In this paper, first, we obtain $L^{\gamma}$ analogue of an inequality concerning a polynomial $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ of degree $n$ having no zero in $\vert z\vert<k$, $k\geq 1$ proved by Govil et al. [Illinois Jour. of Math., 23, No 2 (1979), 319-329].

Second, we also prove $L^{\gamma}$ analogue of another inequality for a polynomial $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ of degree $n$ having all its zeros in $\vert z\vert\leq k$, $k\leq 1$ proved in the same paper. The results improve other known inequalities as well.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 5
Year: 2021

DOI: 10.12732/ijam.v34i5.7

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