On the Value Distribution of the Differential Polynomial Afnf(k) + Bfn+1-1

In the paper, we study the value distribution of the differential polynomial Af(n)f((k)) + Bf(n+1) - 1, where f is a transcendental meromorphic function and n(>= 2), k(not equal 2) are positive integers. We prove an inequality for the Nevanlinna characteristic function T(r, f) in terms of reduced counting function only. The result of the paper not only improves the result due to Q.D. Zhang [J. Chengdu Ins. Meteor., 20(1992), 12-20], also partially improves a recent result of H. Karmakar and P. Sahoo [Results Math., (2018),73:98].

Automated summary

This paper investigates the value distribution of the differential polynomial for transcendental meromorphic functions, proving an inequality for the Nevanlinna characteristic function. The results improve upon previous research and contribute to the field of mathematics.