Affiliation:
1. Department of Mathematics National Institute of Technology Rourkela Rourkela – 769008 INDIA
2. Institut fur Analysis and Algebra TU Braunschweig 38106 Braunschweig GERMANY
Abstract
Abstract
In this paper we answer a question of Bednarz and Sokól concerning concave univalent functions. We prove that there exist central functions for the classes Co(p) of concave univalent functions with pole at the point z = p ∈ (0, 1). Further, we construct a generalized neighborhood of this central function such that the whole class Co(p) is contained in such neighborhood. We also consider similar questions for the class of functions that are analytic and univalent in the unit disc and for some of its important subclasses.
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