In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f ( w ) = f ' ( w ) − 1 = 0 and w a fixed point in U . In 2005, the authors introduced the classes of functions close to convex and α -convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that for w = 0 , the well-known classes of starlike, convex, close-to-convex, and α -convex functions are obtained. In this paper, we continue the investigation of the univalent functions normalized with f ( w ) = f ' ( w ) − 1 = 0 and w , where w is a fixed point in U .