The lecture deals with some basic results of the author in the field of Complex Analysis (Geometric Function Theory of one variable functions) obtained by using the general theory of differential subordinations, and it is connected with some other new results obtained by different authors.

We gave subordination and superordination preserving properties for families of integral operators for meromorphic functions: some applications of the theory of differential subordination, differential superordination, and sandwich-type results for some subclasses of meromorphic functions. It is presented an extensive and detailed application of Pommerenke's result regarding the Löwner chains.

We mention that the first monograph with this topic is those of the author, entitled Differential Subordinations and Superordinations. New Results, House of Scientific Book Publ., Cluj-Napoca, 2005, that appeared just immediately after the first paper that deals with sandwich-type results, that is S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Variables, 2003.

Teodor Bulboacă, Ph.D., D.Sc. works as Full Professor of Mathematics at the Faculty of Mathematics and Computer Science of Babeș-Bolyai University, Cluj-Napoca, Romania. He published more than 130 research articles in the field of Complex Analysis (Geometric Function Theory of one variable functions), and his scientific works were cited in more than 1700 papers according to Google Scholar. Professor Bulboacă is member of the Editorial Board of more than 25 journals, and is the author of the monographs Geometric Function Theory of Univalent Functions (with P. T. Mocanu and Gr. Șt. Sălăgean, House of Science Book Publ., Cluj-Napoca, 1999), Differential Subordinations and Superordinations (House of Science Book Publ., Cluj-Napoca, 2005), and Complex Analysis. Theory and Applications (with S. B. Joshi and P. Goswami, De Gruyter Publ., Berlin, 2019). He delivered lectures as invited speaker, keynote speaker, plenary lecturer to more than 35 international conferences, and participated with talks to more than 100 international conferences.