Properties and characteristics of certain subclasses of starlike functions of order

The authors introduce and investigate the various properties and characteristics of two subclasses H n ( α , β ) and H n + ( α , β ) of starlike functions of order β . In particular, several inclusion relations, Hadamard products, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes. Furthermore, some interesting distortion theorems for the Srivastava–Saigo–Owa fractional integral operator are obtained. Some of the results, presented in this paper, generalize and extend the corresponding results of earlier authors.