The analytic fixed point function II

Published

2006-01-01

The analytic fixed point function II

Keywords:

Fixed point function, Coefficients, Bürmann-Lagrange, Asymptotics, Equilibrium, First return, Branching process, 2000 Mathematics Subject Classification, Primary: 30B10, Secondary: 60F99, 60J80 (en)

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Authors

Universidad Nacional de Colombia (Sede Medellín)
Technische Universität, Berlin

Abstract (en)

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

References

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[KaNa94] A. V. Karpenko & V. Nagaev, Limit theorems for the total number of descendants for the Galton-Watson branching process, Theory Probab. Appl. 38 (1994), 433-455.

[MePo05] D. Mejia & Ch. Pommerenke, The analytic fixed point function in the disk, Comput. Methods Fund. Theory, 5 no. 2 (2005), 275-299.

[Pe75] V. V. Petrov, Sums of independent random variables, Springer, Berlin, 1975.

[PoSz25] G. Pöya & G. Szegö, Aufgaben und Lehrsätze aus der Analysis I, Springer, Berlin, 1925. [Po92] Ch. Pommerenke, Boundary behaviour of conformal maps, Springer, Berlin, 1992.

How to Cite

APA

Diego and Christian. (2006). The analytic fixed point function II. Revista Colombiana de Matemáticas, 40(1), 39–52. https://revistas.unal.edu.co/index.php/recolma/article/view/94669

ACM

[1]

Diego and Christian 2006. The analytic fixed point function II. Revista Colombiana de Matemáticas. 40, 1 (Jan. 2006), 39–52.

ACS

(1)

Diego; Christian. The analytic fixed point function II. rev.colomb.mat 2006, 40, 39-52.

ABNT

DIEGO; CHRISTIAN. The analytic fixed point function II. Revista Colombiana de Matemáticas, [S. l.], v. 40, n. 1, p. 39–52, 2006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94669. Acesso em: 22 jan. 2025.

Chicago

Diego, and Christian. 2006. “The analytic fixed point function II”. Revista Colombiana De Matemáticas 40 (1):39-52. https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Harvard

Diego and Christian (2006) “The analytic fixed point function II”, Revista Colombiana de Matemáticas, 40(1), pp. 39–52. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94669 (Accessed: 22 January 2025).

IEEE

[1]

Diego and Christian, “The analytic fixed point function II”, rev.colomb.mat, vol. 40, no. 1, pp. 39–52, Jan. 2006.

MLA

Diego, and Christian. “The analytic fixed point function II”. Revista Colombiana de Matemáticas, vol. 40, no. 1, Jan. 2006, pp. 39-52, https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Turabian

Diego, and Christian. “The analytic fixed point function II”. Revista Colombiana de Matemáticas 40, no. 1 (January 1, 2006): 39–52. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Vancouver

1.

Diego, Christian. The analytic fixed point function II. rev.colomb.mat [Internet]. 2006 Jan. 1 [cited 2025 Jan. 22];40(1):39-52. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/94669