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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2017},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a6/}
}
TY  - JOUR
AU  - S. Yu. Graf
AU  - Ya. I. Samoylova
TI  - On regularity of decreasing of convexity order in $C(\alpha)$ classes
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2017
SP  - 85
EP  - 99
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a6/
LA  - ru
ID  - VTPMK_2017_4_a6
ER  - 
%0 Journal Article
%A S. Yu. Graf
%A Ya. I. Samoylova
%T On regularity of decreasing of convexity order in $C(\alpha)$ classes
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2017
%P 85-99
%N 4
%U http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a6/
%G ru
%F VTPMK_2017_4_a6
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/

[1] Robertson M. I. S., “On the theory of univalent functions”, Annals of Mathematics, 37:2 (1936), 374-408 | DOI | MR

[2] Mocanu P. T., “Une properiété de convexité généralisée dans la théorie de la représentation conforme”, Mathematica, 11:34 (1969), 127-133 | MR | Zbl

[3] Goodman A. W., “On uniformly convex functions”, Annales Polonici Mathematici, 1991, no. 56, 87-92 | DOI | MR | Zbl

[4] Duren P., Univalent functions, Springer-Verlag, N.Y., 1983, 395 pp. | MR | Zbl

[5] Graf S. Yu., Samoilova Ya. I., “Regularity of decreasing convexity order and hyperbolic order of convexity of conformal mappings”, Application of Functional Analysis in Approximation Theory, 2016, no. 37, 13-27 (in Russian)

[6] Kheiman V. K., Multivalent Functions, Inostrannaya literatura, Moscow, 1960, 180 pp. (in Russian) | MR

[7] Krzyz J., “On the maximum modulus of univalent functions”, Bull. Acad. Polonici Sci, CI:3 (1955), 203-206 | MR

[8] Goluzin G. M., Geometric Theory of Functions of a Complex Variable, Moscow, 1966, 628 pp. (in Russian) | MR

[9] Ganenkova E. G., “A theorem of regularity of decrease in linearly invariant families of functions”, Proceedings of Petrozavodsk State University. Series: Mathematics, 2006, no. 13, 46-59 (in Russian) | MR

[10] Ganenkova E. G., Starkov V. V., “Regularity theorems for harmonic functions”, Journal of Applied Analysis, 21:1 (2015), 25-36 | DOI | MR | Zbl

[11] Graf S. Yu., “Regularity theorems for the Jacobian in linear and affine-invariant families of harmonic maps”, Application of Functional Analysis in Approximation Theory, 2014, no. 35, 10-21 (in Russian)

[12] Graf S. Yu., Samoylova Ya. I., “Regularity of decreasing of convexity order in the class of conformal mappings”, Vestnik TvGU. Seriya: Prikladnaya matematika [Herald of Tver State University. Series: Applied Mathematics], 2015, no. 2, 135-145 (in Russian)