S. Yu. Graf, Ya. I. Samoylova, “On regularity of decreasing of convexity order in <nobr>$C(\alpha)$</nobr> classes”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2017, Issue 4,Pages <nobr>85

Real, Complex and Functional Analysis

On regularity of decreasing of convexity order in $C(\alpha)$ classes

S. Yu. Graf^ab, Ya. I. Samoylova^ba

^a Tver State University, Tver
^b Petrozavodsk State University, Petrozavodsk

Abstract: 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.

UDC: 517.54

Received: 27.07.2017
Revised: 20.10.2017

DOI: 10.26456/vtpmk191