Third order differential subordination and superordination results for analytic functions involving the Hohlov operator

The problems of third order differential subordination as well as superordination for functions analytic in the open unit disk seem to be new and have been of interest after the seminal work of Antonino and Miller, and Tang. In the present paper by considering suitable classes of admissible functions associated with Hohlov operator, various third order differential subordination as well as differential superordination results are obtained. As a consequence, the dual problems which gives the sandwich-type relations are presented. Upon suitable choice of the parameters, the results obtained in this paper include some classical as well as recently studied results. An attempt has also been made to illustrate the applications of the new results in the context of electromagnetic cloaking problem.