Subclasse of starlike and convex functions associated to domain bounded by a nephroid

One of the most important and interesting topics in the geometric function theory is the classes of starlike and convex functions of Ma-Minda type on the unit disk D = {z ∈ C: |z| < 1} which are defined by subordination. Let A be the class of functions f, analytic in the unit disc D = {z : |z| < 1} on the complex plane C, with the normalization f(0) = f 0 (0) − 1 = 0, and ST N (s) and CVN (s) be a family of starlike and convex functions f ∈ A so that for each z ∈ D, such that the quantity zf0 (z)/f(z) or 1 + zf00(z)/f0 (z) respectively are lying in the region bounded by the Nephroid (u − 1)2 + v 2 − 4s 2 3 = 108s 4 v 2 , 0 < s ≤ √ 2 4 . In this paper, some properties and characteristics of classes ST N (s) and CVN (s) defined by the Ma-Minda type, like the structure of functions in these classes, we study extreme functions, growth theorem, distoration, and rotation theorem.