Certain Estimates of Normalized Analytic Functions

Abstract

Let ϕ be a normalized convex function defined on open unit disk D . For a unified class of normalized analytic functions which satisfy the second order differential subordination f′(z) + αzf″(z) ≺ ϕ(z) for all z ∈ D , we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient and the second Hankel determinant involving the inverse coefficients are examined.

Radii Constants for Functions with Fixed Second Coefficient

“…Several well known subclasses of starlike functions were characterized by subordination of zf ′ /f to some function in P. Using a function ψ, univalent in unit disc ∆ with Re(ψ(z)) > 0, starlike with respect to ψ(0) = 1, symmetric about the real axis and ψ ′ (0) > 0, Ma and Minda [20] gave a unified treatment for several subclasses of starlike functions by studying the class S * (ψ) ={ f ∈ A : zf ′ (z)/f (z) ≺ ψ(z)}. Recently, Anand et al [7] also obtained some results for a class of analytic functions defined using the function ψ. Several authors considered the class S * (ψ) for various choices of the function ψ.…”