D. R. Bhat

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math.CV2026

Inequalities Concerning Rational Functions With Prescribed Poles

N. A. Rather, Tanveer Bhat, Danish Rashid Bhat

Let $ℜ_{n}$ be the set of all rational functions of the type $r (z) = p (z) / w (z),$ where $p (z)$ is a polynomial of degree at most $n$ and $w (z) = \prod_{j = 1}^{n} (z - a_{j})$ , $∣ a_{j} ∣ > 1$ f…

math.CV2025

A Note On Generalized $L_{p}$ Inequalities for the polar derivative of a polynomial

N. A. Rather, Danish Rashid Bhat, Tanveer Bhat

Let $ P(z) $ be a polynomial of degree $ n $ and $α \in C$ . The polar derivative of $ P(z) $, denoted by $ D_αP(z) $ and is defined by $D_αP(z): = nP(z) + (α-z)P'(z…

math.CV2025

A refinement of Cauchys theorem on the zeros of quaternion polynomial

Nisar Ahmad Rather, Danish Rashid Bhat, Tanveer Bhat

In this paper, we shall present an interesting and significant refinement of a classical result of Cauchy about the moduli of the zeros of a quaternionic polynomial. As an applicat…

Inequalities Concerning Rational Functions With Prescribed Poles

A Note On Generalized Lp​ Inequalities for the polar derivative of a polynomial

A refinement of Cauchys theorem on the zeros of quaternion polynomial

A Note On Generalized $L_{p}$ Inequalities for the polar derivative of a polynomial