Directional convexity of level lines for functions convex in a given direction期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Directional convexity of level lines for functions convex in a given direction

Authors:	Dmitri V. Prokhorov Jan Szynal

Affiliation:	Department of Mathematics, Saratov State University, 410026 Saratov, Russia ; Department of Mathematics, M. Curie-Sklodowska University, 20-031 Lublin, Poland

Abstract:	Let be the class of functions $f(z)=z+a_{2}z^{2}+dots$ which are holomorphic and convex in direction $e^{ivarphi }$ in the unit disk , i.e. the domain is such that the intersection of and any straight line ${w:w=w_{0}+te^{ivarphi },tin mathbb{R}}$ is a connected or empty set. In this note we determine the radius $r_{psi ,varphi }$ of the biggest disk $vert zvertleq r_{psi ,varphi }$ with the property that each function maps this disk onto the convex domain in the direction $e^{ivarphi }$ .

Keywords:	Level curves of holomorphic functions functions convex in one direction

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