On certain problem in the class of kk-starlike functions

In this paper we consider the classes of kk-uniformly convex and kk-starlike functions defined in Kanas and Wiśniowska (1999, 2000) [1] and [2] which generalize the class of uniformly convex functions introduced by Goodman (1991) [3]. We discuss the real part of f(z)/zf(z)/z, when ff is kk-starlike. We find the minimum of Ref(z)/zRef(z)/z improving the results obtained recently in Wiśniowska-Wajnryb (2009) [11].