Abstract

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.