Some uniqueness results related to the Br\"{u}ck Conjecture

TL;DR

This paper investigates conditions under which a meromorphic function and its differential polynomial sharing a small function lead to conclusions related to the Bruck Conjecture, extending previous results.

Contribution

It generalizes and improves recent results by establishing new conditions for the Bruck Conjecture involving differential polynomials sharing small functions.

Findings

Established new conditions for the Bruck Conjecture involving differential polynomials.

Extended previous results by Li, Yang, and Liu.

Provided a more general framework for sharing small functions in meromorphic functions.

Abstract

Let f be a non-constant meromorphic function and a = a(z) be a small function of f. Under certain essential conditions, we obtained similar type conclusion of Bruck Conjecture, when f and its differential polynomial P[f] shares a with weight l. Our result improves and generalizes a recent result of Li, Yang, and Liu.