Abstract
For lambda satisfying a certain admissibility criteria, sufficient conditions are obtained that ensure the integral transform
V(lambda)(f)(z) := integral(1)(0)lambda(t)f(tz)/tdt
maps normalized analytic functions f satisfying
Ree(i phi)((1 - alpha + 2 gamma)f(z)/z + (alpha - 2 gamma)f'(z) + gamma zf ''(z)-beta) > 0
into the class of starlike functions. Several interesting examples of lambda are considered. Connections with various earlier works are made, and the results obtained not only reduce to those earlier works, but indeed improved certain known results. As a consequence, the smallest value beta < 1 is obtained that ensures a function f satisfying Re(f'(z) + alpha zf ''(z) + gamma z(2)f'''(z)) > beta is starlike. (C) 2011 Elsevier Inc. All rights reserved.