Abstract

MEJIA, Diego  and  POMMERENKEY, Christian. THE ANALYTIC FIXED POINT FUNCTION II. Rev.colomb.mat. [online]. 2006, vol.40, n.1, pp.39-52. ISSN 0034-7426.

Let φ be analytic in the unit disk D and let φ(D) ⊂ D, φ(0) 6= 0. Then w = z/φ(z) has an analytic inverse z = f(w) for w ∈ D, the fixed point function. This paper studies the case that φ(1) = φ´(1) = 1 with a growth condition for φ´´(x) and determines the asymptotic behaviour of various combinations of the coefficients of φ connected with f. The results can be interpreted in various contexts of probability theory.

Keywords : Fixed point function; coefficients; Bürmann-Lagrange; asymptotics; equilibrium; first return; branching process.

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