  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].
