Criteria for Strongly Starlike Functions. (3rd July 2011)

• Record Type: Journal Article
• Authors: Xu, Neng
• Other Names: Belhaj A. Academic Editor.; Ungar A. A. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2011(2011)
• Publication Date: 2011-07-03
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.5402/2011/151474
• Languages: English
• ISSNs: 2090-6307

Abstract

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.