On Certain Subclass of Starlike Functions with Two Fixed Points

Abstract

Let ST_λ(n, α, z₀) be the class of functions o f the form

                              f(z) = a₁z-Σa_mz^m,

where a_m ≥ 0 and a₁ > 0, analytic in the unit disc

E = {z :|z| < 1 ) and F(z) = 2/z∫ f(t)dt

satisfying (1-λ) F(Z₀)/Z₀ + λF'(Z₀) = 1; 0≤λ≤1, -1<Z₀<1.

such that Re {Dⁿ⁺¹f(Z)/Dⁿf(Z)} > α|Dⁿ⁺¹f(Z)/Dⁿf(Z)-1|, α≥0

where D is the Ruscheweyh derivative o f f(Z). Properties of functions in STλ(n, α Z₀) such as coefficient estimate, closure theorem, extreme points and radius of convexity are determined.