Bulletin of the
Korean Mathematical Society BKMS

In the present paper sufficient conditions, in terms of hypergeometric inequalities, are found so that the Hohlov operator preserves a certain subclass of close-to-convex functions (denoted by ${\mathcal {R}}^\tau(A,B)$) and transforms the classes consisting of $k$-uniformly convex functions, $k$-starlike functions and univalent starlike functions into ${\mathcal {R}}^\tau(A,B)$.

Keywords: univalent, $k$-uniformly convex, parabolic starlike, hypergeometric series, Hadamard product, Hohlov operator

MSC numbers: 30C45, 33E05