A note on the value distribution of $\phi f^2 f^{(k)}-1$

P. Sahoo; G. Biswas

doi:10.30970/ms.55.1.64-75

P. Sahoo University of Kalyani, West Bengal-741235, India
G. Biswas Hooghly Women’s College, West Bengal-712103, India

DOI: https://doi.org/10.30970/ms.55.1.64-75

Keywords: Meromorphic function, Differential polynomial, Nevanlinna theory, Value distribution

Abstract

In this paper, we study the value distribution of the differential polynomial $\varphi f^2f^{(k)}-1$, where $f(z)$ is a transcendental meromorphic function, $\varphi (z)\;(\not\equiv 0)$ is a small function of $f(z)$ and $k\;(\geq 2)$ is a positive integer. We obtain an inequality concerning the Nevanlinna Characteristic function $T(r,f)$ estimated by reduced counting function only. Our result extends the result due to J.F. Xu and H.X. Yi [J. Math. Inequal., 10 (2016), 971-976].

Author Biographies

P. Sahoo, University of Kalyani, West Bengal-741235, India

Department of Mathematics, University of Kalyani, West Bengal-741235, India

G. Biswas, Hooghly Women’s College, West Bengal-712103, India

Department of Mathematics, Hooghly Women’s College, West Bengal-712103, India

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