Abstract
For the function f(z) analytic in the open unit disk and normalized by f(0) = f0(0)−1 = 0, we consider the expression; ( zf0(z)f(z)−1)+1−( zf(z) );( > 0). Using differential subordination notion, we investigate properties of ( f(z) z ) , as well as, sufficient conditions for univalence and starlikeness of f(z). In the special case, for = 1, these results generalize and improve some previously results given in the literature.
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