Entire Functions Sharing Small Functions With Their Difference Operators

TL;DR

This paper studies when entire functions are uniquely determined by their sharing of small functions with their difference operators, extending previous results in the field.

Contribution

It generalizes existing theorems on entire functions sharing small functions with their difference operators, broadening the scope of known uniqueness results.

Findings

Established new conditions for entire functions sharing small functions with their difference operators.

Extended previous theorems to more general cases.

Provided a broader framework for understanding uniqueness in difference operator contexts.

Abstract

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.