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(۰) = f۰(۰)−۱ = ۰, we consider the expression; ( zf۰(z)f(z)−۱)+۱−( zf(z) );( > ۰). 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  = ۱, these results generalize and improve some previously results given in the literature.

Keywords:

Differential subordination , Univalent , Starlike , Close-to-convex