Criteria for Strongly Starlike Functions. (3rd July 2011) - Xu, Neng
Abstract : Letf ( z ) be analytic in the unit diskU = { z : | z | < 1 } withf ( 0 ) = f ' ( 0 ) - 1 = 0 and(f ( z ) / z) f ' ( z ) ≠ 0 . By using the method of differential subordinations, we determine the largest numberα ( β, λ, μ, m ) such that, for someβ, λ, μ, andm, the differential subordinationλ z f ' ( z ) / f ( z ) 1 - μ 1 +( z f ' ' ( z ) / f ' ( z ) )- z f ' ( z ) / f ( z ) + z f ' ( z ) / f ( z ) m ≺ 1 + z / 1 - z α ( β, λ, μ, m ) ( z ∈ U ) impliesz f ' ( z ) / f ( z ) ≺ 1 + z / 1 - z β . Some useful consequences of this result are also given.