a new subclass of univalent functions associated with the limacon domain

Let a denote the family of analytic and normalized functionsf(z) = z +ó1n=2 anzn in the unit disk d := fz : jzj < 1g, such that f(z) =u + iv lies in a domain bounded by a limacon[(u .. 1)2 + v2 .. s2t2]2= (t .. s)2[(u .. 1 .. st)2 + v2];where ..1  s < t  1 and 0 < 2jstj  t .. s. in this work, we introduce afamily of analytic univalent functions in the open unit disc d. for functionsbelonging to this class, we derive several properties such as bounded for realpart and the order of starlikeness and convexity.