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)+ α z f''(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.