# Inequalities for B-operator

## Main Article Content

## Abstract

Let $\mathcal{P}_n$ denote the space of all complex polynomials $P(z)=\sum\limits_{j=0}^{n}a_j z^j$ of degree $n$. Let $P\in\mathcal{P}_n$, for any complex number $\alpha$, $D_\alpha P(z)=nP(z)+(\alpha -z)P'(z)$, denote the polar derivative of the polynomial $P(z)$ with respect to $\alpha$ and $B_n$ denote a family of operators that maps $\mathcal{P}_n$ into itself. In this paper, we combine the operators $B$ and $D_\alpha$ and establish certain operator preserving inequalities concerning polynomials, from which a variety of interesting results can be obtained as special cases.

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