A Class of Analytic Functions with Missing Coefficients.

Let Tn(A, B, γ, α) (-1 ≤ B < 1, B < A, 0 < γ ≤ 1 and α > 0) denote the class of functions of the form f(z) = z + ∑Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.akzk (n ∈ N = {1, 2, 3,…}), which are analytic in the open unit disk U and satisfy the following subordination condition f'(z) + αzf" (z) < ((1 + Az)/(1 + Bz))γ, for (z ∈ U;A ≤ 1; 0 < γ < 1), (1 + Az)/(1 + Bz), for (z ∈ U; γ = 1). We obtain sharp bounds on Ref' (z), Ref(z)/z, |f(z)|, and coefficient estimates for functions f(z) belonging to the class Tn(A, B, γ, α). Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered. [ABSTRACT FROM AUTHOR]