Geodesic
On regularity of decreasing of convexity order in $C(\alpha)$ classes
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2017), pp. 85-99

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In the present paper the new regularity theorems for order of convexity and hyperbolic order of convexity in the classes of convex conformal mappings of order $\alpha$ in the unit disk are proved. The sharpness of the result is illustrated by several examples.
Keywords: conformal mappings, convex mappings, order of convexity, regularity theorems. 
@article{VTPMK_2017_4_a6,
     author = {S. Yu. Graf and Ya. I. Samoylova},
     title = {On regularity of decreasing of convexity order in $C(\alpha)$ classes},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {85--99},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a6/}
}
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S. Yu. Graf; Ya. I. Samoylova. On regularity of decreasing of convexity order in $C(\alpha)$ classes. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2017), pp. 85-99. http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a6/