Starlike and Convex Functions Associated with a Nephroid Domain

In this paper, we show that the Caratheodory function phi Ne(z)=1+z-z3/3 onto the interior of the nephroid, a 2-cusped kidney-shaped curve, and introduce new Ma-Minda-type function classes SNeand CNeassociated with it. Apart from studying the characteristic properties of the region bounded by this nephroid, the structural formulas, extremal functions, growth and distortion results, inclusion results, coefficient bounds and Fekete-Szego problems are discussed for the classes SNe* and CNe. Moreover, for beta is an element of R and some analytic function p(z) satisfying p(0)=1, we prove certain subordination implications of the first-order differential subordination 1+beta zp '(z)/pj(z)& x227a;phi Ne(z),j=0,1,2, and obtain sufficient conditions for some geometrically defined function classes available in the literature.