Certain Estimates of Normalized Analytic Functions

Abstract

Let $\ddot{I}•$ be a normalized convex function defined on open unit disk $\mathbb{D}$. For a unified class of normalized analytic functions which satisfy the second order differential subordination $f^{\prime }(z)+\hat{I}\pm z{f}^{\prime \prime }(z)\prec \ddot{I}•(z)$ for all $z\in \mathbb{D}$, 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.