Uniqueness of Meromorphic functions concerning k-th derivatives and difference operators

TL;DR

This paper investigates the uniqueness of meromorphic functions when sharing values with their higher derivatives and difference operators, extending previous results and providing more general conditions.

Contribution

It generalizes and improves existing results on the sharing value problems for higher derivatives and difference operators of meromorphic functions.

Findings

Extended the class of functions for which uniqueness holds

Provided new conditions under which sharing value problems are solved

Improved bounds and generalized previous theorems

Abstract

In this paper, we continue to study the sharing value problems for higher order derivatives of meromorphic functions with its linear difference and $q$-difference operators. Some of our results generalize and improve the results of Meng--Liu (J. Appl. Math. and Informatics, 37(2019), 133--148) to a large extent.