Linear Delay-Differential operator of a meromorphic function sharing two sets or small function together with values with its $c$-shift or $q$-shift

TL;DR

This paper investigates the uniqueness of linear delay-differential operators of meromorphic functions sharing specific sets or small functions with their $c$-shift and $q$-shift, improving previous results in the field.

Contribution

It provides new theorems that significantly enhance existing results on the uniqueness of such operators, extending the scope of prior work.

Findings

Improved bounds for sharing sets or functions between meromorphic functions and their shifts.

Extended previous theorems to broader classes of functions and operators.

Established new uniqueness criteria that unify and generalize earlier results.

Abstract

The paper is devoted to study the uniqueness problem of linear delay-differential operator of a meromorphic function sharing two sets or small function together with values with its $c$-shift and $q$-shift operator. Results of this paper drastically improve two recent results of Meng-Liu [J. Appl. Math. Inform. 37(1-2)(2019), 133-148] and Qi-Li-Yang [Comput. Methods Funct. Theo., 18(2018), 567-582]. In addition to this, one of our result improve and extend that of Qi-Yang [Comput. Methods Funct. Theo., 20(2020), 159-178].