Some applications of differential subordination and the Dziok–Srivastava convolution operator

By making use of the principle of differential subordination and the Dziok–Srivastava convolution operator, we introduce and investigate three interesting subclasses of analytic and univalent functions in the open unit disk. We obtain their inclusion relationships and also show that these classes are closed under convolution with convex functions. The results presented in this paper provide generalizations of several recent works by (for example) Özkan and Altıntaş (2006) [16], Trojnar-Spelina (2008) [30], and many other authors.