some generalized results based on differential subordinations of analytic functions

For the function f(z) analytic in the open unit disk and normalized by f'(0) = f0(0)−1 = 0, we consider the expression; α( zf'(z)/f(z)−1)+1−( z/f(z) )α;( α> 0). using differential subordination notion, we investigate properties of ( f(z)/ z )α, as well as, sufficient conditions for univalence and starlikeness of f(z). in the special case, for α= 1, these results generalize and improve some previously results given in the literature.