Calculation of the Hessian for the Log-Log Frequency Distribution
We calculate the diagonal entries of the Hessian for our log-log frequency models.
On a class of -convex functions.
In this paper we define a general class of α-convex functions with respect to a convex domain D contained in the right half plane by using a generalized Sălăgean operator introduced by F.M. Al-Oboudi in [5] and we give some properties of this class. 2000 Mathematical Subject Classification: 30C45
On a subclass of n-starlike functions
In 1999, Kanas and Ronning 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.