D. R. Bhat

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math.CV2026

Inequalities For The Growth Of Rational Functions With Prescribed Poles

N. A. Rather, Mohmmad Shafi Wani, Danish Rashid Bhat

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

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 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…