Generalized Alpha-Close-to-Convex Functions. (15th October 2009) - Noor, K. Inayat; Orhan, Halit; Mustafa, Saima
Abstract : We define the classesG β ( α, k, γ ) as follows:f ∈ G β ( α, k, γ ) if and only if, forz ∈ E = z ∈ ℂ : | z | < 1 , | arg ( 1 - α 2 z 2 ) f ′ ( z ) / e − i β ϕ ′ ( z ) | ≤ γ π / 2, 0 < γ ≤ 1 ;α ∈ [ 0, 1 ] ;β ∈ ( − π / 2, π / 2 ), whereϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other properties of these classes are studied.