Convexity constant of a domain and applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Pascu, Nicolae R.¹  Pascu, Mihai N.² 

[1] Kennesaw State Univ, Dept Math, 1100 S Marietta Pkwy, Marietta, GA 30060 USA

[2] Transilvania Univ Brasov, Fac Math & Comp Sci, Dept Math & Comp Sci, Str Iuliu Maniu 50, Brasov 500091, Romania

关键词: Convex set;    Convexity constant of a domain;    Univalent function;    Univalence criterion;   

DOI  :  10.1016/j.jmaa.2016.12.024

来源: Elsevier

【 摘 要 】

In the present paper we introduce a new characterization of the convexity of a planar domain, based on the convexity constant K (D) of a domain D subset of C. We show that in the class of simply connected planar domains, K (D) = 1 characterizes the convexity of the domain D, and we derive the value of the convexity constant for some classes of doubly connected domains of the form D-Omega = D - (Omega) over bar for certain choices of the domains D and Omega. Using the convexity constant of a domain, we derive an extension of the well-known Ozaki-Nunokawa-Krzyz univalence criterion for the casFs of non-convex domains, and we present some examples, which show that our condition is sharp. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free