Geodesic
The Sharp upper bound for $\mathfrak{R}(A_{3}-\lambda A_{2})$ in $U'_{\alpha}$
Problemy analiza, no. 15 (2008), pp. 17-23.

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In this note we determine the exact value of max $\mathfrak{R}(A_{3}-\lambda A_{2}), \lambda \in \mathbb{R}$, within the linearly invariant family $U'_{\alpha}$ introduced by V. V. Starkov in [4]. For $\lambda = 0$ the sharp estimate for $|A_{3}|$ follows. If $\alpha = 1$ the corresponding result is valid for convex univalent functions in the unit disk. 
@article{PA_2008_15_a3,
     author = {I. Naraniecka},
     title = {The {Sharp} upper bound for $\mathfrak{R}(A_{3}-\lambda A_{2})$ in $U'_{\alpha}$},
     journal = {Problemy analiza},
     pages = {17--23},
     publisher = {mathdoc},
     number = {15},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2008_15_a3/}
}
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I. Naraniecka. The Sharp upper bound for $\mathfrak{R}(A_{3}-\lambda A_{2})$ in $U'_{\alpha}$. Problemy analiza, no. 15 (2008), pp. 17-23. http://geodesic.mathdoc.fr/item/PA_2008_15_a3/