Uniqueness of an entire function sharing two values jointly with its differential polynomials

TL;DR

This paper explores the uniqueness of entire functions sharing two values with their differential polynomials or monomials, extending previous results in complex analysis.

Contribution

It generalizes recent findings by analyzing the joint sharing of two values between entire functions and their differential polynomials or monomials.

Findings

Extended uniqueness results for entire functions sharing two values with their differential polynomials.

Generalized Lahiri's recent results in the context of value sharing.

Provided conditions under which entire functions are uniquely determined by shared values.

Abstract

In this paper, we continue to investigate the uniqueness problem when an entire function $f$ and its linear differential polynomial $L(f)$ share two distinct complex values CMW (counting multiplicities in the weak sense) jointly. Also, We investigate the same problem when $f$ and its differential monomial $M(f)$ share two distinct complex values CMW. Our results generalize the recent result of Lahiri (Comput. Methods Funct. Theory, https://doi.org/10.1007/s40315-020-00355-4).