Some Inequalities of differential polynomials II

TL;DR

This paper investigates the value distribution of specific differential polynomials, providing new estimates that resolve a previously posed question in the field of mathematical inequalities.

Contribution

It offers novel estimates for the value distribution of differential polynomials, specifically addressing a question from prior research.

Findings

Established new estimates using reduced counting functions

Answered a previously open question completely

Contributed to the understanding of differential polynomial value distribution

Abstract

In this paper, we consider the value distribution of the differential polynomials $f^2f^{(k)}-1$ where $k$ is a positive integer, and obtain some estimates only by the reduced counting function. Our result answers a question in (Some inequalities of differential polynomials, Mathematical Inequalities and Applications, \textbf{12}(2009), no.1, 99--113) completely.