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http://dx.doi.org/10.11568/kjm.2022.30.3.525

INEQUALITIES FOR B-OPERATOR  

Akhter, Rubia (Department of Mathematics, University of Kashmir)
Gulzar, M.H. (Department of Mathematics, University of Kashmir)
Publication Information
Korean Journal of Mathematics / v.30, no.3, 2022 , pp. 525-532 More about this Journal
Abstract
Let 𝓟n denote the space of all complex polynomials $P(z)=\sum\limits_{j=0}^{n}{\alpha}_jz^j$ of degree n. Let P ∈ 𝓟n, for any complex number α, DαP(z) = nP(z) + (α - z)P'(z), denote the polar derivative of the polynomial P(z) with respect to α and Bn denote a family of operators that maps 𝓟n into itself. In this paper, we combine the operators B and Dα and establish certain operator preserving inequalities concerning polynomials, from which a variety of interesting results can be obtained as special cases.
Keywords
B-operator; Polar Derivative; Zeros; Inequalities;
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