Research ArticleNo Access

On some operator preserving inequalities between polynomials

Shabir Ahmad Malik

Department of Mathematics, University of Kashmir, Srinagar 190006, India

E-mail Address: shabirams2@gmail.com

Corresponding author.

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and

Bashir Ahmad Zargar

Department of Mathematics, University of Kashmir, Srinagar 190006, India

E-mail Address: bazargar@gmail.com

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https://doi.org/10.1142/S1793557123501978Cited by:0 (Source: Crossref)

Abstract

In this paper, some generalizations of lower bound estimates for the maximum modulus of the $t$ th polar derivative $D_{ξ_{t}} D_{ξ_{t - 1}} \dots D_{ξ_{2}} D_{ξ_{1}}$ , where $ξ_{t} \in ℂ$ , $1 \leq t < n$ of polynomials are established under the assumption that one of the underlying polynomials $p$ and $q$ does not vanish in $| z | > k, k \leq 1$ . The obtained estimates include several known lower bounds for polar derivatives as special cases.

Communicated by S.R. Sharama

Keywords:

AMSC: 30A10, 30C10, 30C15, 30C99

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