The order of close-to-convexity for certain univalent functions (Q1824717)

Suppose that \(f(z)=z+\sum^{\infty}_{k=n+1}a_ kz^ k\) is a function locally univalent and analytic in the unit disc D, g(z) is a function convex and univalent in D. For a given real \(\alpha\) the author determines \(\beta\) (\(\alpha)\) such that the relation \[ Re\{1+(zf''(z)/f'(z))\}>\alpha \quad \Rightarrow \quad Re\{f'(z)/g'(z)\}>\beta (\alpha) \] holds in D.