Abstract
Let φ be analytic in the unit disk D and let φ(D) ⊂ D, φ(0) ≠ 0. Then ω = z/φ(z) has an analytic inverse z = f(ω), ω ∈ D, the fixed point function. Here f(D) is a starlike domain and various results suggest that f(D) might even be hyperbolically convex. We study the derivative and the coefficients of f, in particular their asymptotic behaviour. In the case that φ is the generating function of a random variable, several functions related to f have probabilistic interpretations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.