Open AccessA note on the value distribution of $\phi f^2 f^{(k)}-1$
Author(s) -
Pulak Sahoo,
Gurudas Biswas
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.55.1.64-75
Subject(s) - meromorphic function , mathematics , function (biology) , entire function , transcendental function , distribution (mathematics) , combinatorics , polynomial , value (mathematics) , integer (computer science) , transcendental number , pure mathematics , mathematical analysis , statistics , evolutionary biology , computer science , biology , programming language
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].