doiSerbia

Sharp estimates of generalized zalcman functional of early coeffcients for Ma-Minda type functions

Cho Nak Eun
Kwon Oh Sang
Lecko Adam
Sim Young Jae

Let φ be an analytic function in the unit disk D := {z ϵ C : |z| < 1} which has the form φ(z) = 1 + p1z + p2z2 + p3z3 + ... with p1 > 0, p2, p3 ϵ R. For given such φ, let S*(φ), K(φ) and R(φ) denote the classes of standardly normalized analytic functions f in D which satisfy zf'(z)/f(z) < φ(z), 1 + zf''(z)/f'(z) < φ(z) f'(z)< φ(z), z ϵ D, respectively, where < means the usual subordination. In this paper, we find the sharp bounds of |a2a3-a4|, where an := f(n)(0)/n!; n ϵ N, over classes S*(φ), K(φ) and R(φ).

Keywords: coefficient estimate, subordination, starlike function, convex function, function of bounded turning