Comparative growth analysis of special type of differential polynomial generated by entire and meromorphic functions on the basis of their (p,q)-th order

TL;DR

This paper investigates the growth behavior of certain differential polynomials generated by entire and meromorphic functions, based on their (p,q)-th order and lower order, providing new comparative growth results.

Contribution

It introduces new results on the comparative growth of differential polynomials generated by entire and meromorphic functions using (p,q)-th order analysis.

Findings

Established inequalities relating growth of functions and their differential polynomials

Extended growth comparison to (p,q)-th order and lower order frameworks

Provided conditions under which differential polynomials exhibit specific growth behaviors

Abstract

In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on the basis of (p,q)-th order and (p,q)-th lower order where p,q are positive integers with p greater than or equal to q.