Univalency, starlikeness and convexity applied to certain classes of rational functions

Let S, <S∗(a) and K(a) denote the usual classes of normalized analytic functions f that are respectively univalent, starlike of order a and convex of order a. Define This paper concerns the following problems which also led to a proof of two conjectures of Ponnusamy and Obradovic:. © 2014, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All rights reserved.