In this article, by making use of the linear operator introduced and studiedby Srivastava and Attiya \cite{srivastava1}, suitable classes of admissiblefunctions are investigated and the dual properties of the third-orderdifferential subordinations are presented. As a consequence, varioussandwich-type theorems are established for a class of univalent analyticfunctions involving the celebrated Srivastava-Attiya transform. Relevantconnections of the new results are pointed out.