The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary
The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name.
Authors: .
Let f(z) = a1z+a1z2 +... , a1≠ 0, be regular in |z| < 1 and have there no zeros except at the origin. Reade ([3]) and the Sakaguchi ([2]) showed that a necessary and sufficient condition for f(z) to be a member of the class C(k) is that f(z) has a representation of the form
f(z) = s(z)(p(z))k
where s(z) is a regular function starlike with respect to the origin for |z| < 1, k is a positive constant, and p(z) is a regular function with positive real part in |z| < 1. The class of close-to-star functions introduced by Reade ([4]) is equivalent to C(1). In this paper we define the class C(k, A,B) (−1 £ B < A £ 1, k is positive constant) which contains the functions of the form
f(z) = s(z)(p(z))k
where s(z) is a regular Janowski starlike function, and p(z) is a regular functionwith positive real part in |z| < 1. The aim of this paper is to give some propertiesand distortion theorems for this class.
Mathematics Subject Classification (2010): 30C45.
Keywords: Distortion theorem, radius of starlikeness.
