Some simple sufficient conditions for starlikeness and convexity

Let A be the class of analytic functions in the unit disc that are of the form f(z) = z + a(2)z(2) + ..... In this work the expressions f'(z) - (1 - gamma)f(z)/z and zf ''(z) - gamma f'(z), 0 < y <= are studied, as sufficient conditions for starlikeness and convexity. (c) 2008 Elsevier Ltd. All rights reserved.