On the uniqueness of power of a meromorphic function sharing a set with its k-th derivative

TL;DR

This paper investigates the uniqueness of powers of meromorphic functions when they share a set with their k-th derivatives, extending previous value-sharing results to more general set-sharing scenarios.

Contribution

It introduces a broader set-sharing framework to analyze the uniqueness of meromorphic functions and their derivatives, advancing the understanding beyond value sharing.

Findings

Established conditions for uniqueness under set sharing

Extended previous results to more general sharing scenarios

Provided new theorems on meromorphic function uniqueness

Abstract

In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing