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The problem of estimating the radius of starlikeness of various classes of close-to-convex functions has attracted a certain number of mathematicians involved in geometric function theory ([7], volume 2, chapter 13). Lewandowski [11] has shown that normalized close-to-convex functions are starlike in the disc $\left|z\right|<4\surd 2-5$. Krzyż [10] gave an example of a function $f\left(z\right)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$, non-starlike in the unit disc , and belonging to the class H = f | f’() lies in the right half-plane. More generally let H* = f | f’() lies in...