Unique range sets of meromorphic functions of non-integer finite order

TL;DR

This paper investigates the uniqueness of certain non-integer order meromorphic functions sharing finite sets, addressing a question by Gross and analyzing related recent results in the field.

Contribution

It introduces new results on the uniqueness of non-integer finite order meromorphic functions sharing finite sets and provides insights into a question posed by Gross.

Findings

Established conditions for the uniqueness of meromorphic functions sharing finite sets.

Provided an answer to Gross's question for a specific class of meromorphic functions.

Made observations on recent related results by Sahoo and colleagues.

Abstract

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic functions. Moreover, some observations are made on some results due to Sahoo and Karmakar ( Acta Univ. Sapientiae, Mathematica, DOI: 10.2478/ausm-2018-0025) and Sahoo and Sarkar (Bol. Soc. Mat. Mex., DOI: 10.1007/s40590-019-00260-4).