Certain Ma–Minda type classes of analytic functions associated with the crescent-shaped region

In this paper, we study certain classes of analytic functions which satisfy a Ma–Minda type subordination condition and are associated with the crescent-shaped region. We first give the extremal functions of these function classes and related to them, we present various characteristic properties. It is shown that for certain range of coefficients, a bilinear transformation belongs to a certain class (defined below). Also, for this and related classes, we present certain results and give some specific examples. Further, we obtain results on coefficient inequalities and coefficient estimates. Finally, using the subordination theory, we derive various results and corollaries for functions belonging to the classes studied in this paper.