Compositions of analytic functions of the form \(F_ n(z)=F_{n-1}(f_ n(z))\), \(f_ n(z)\to f(z)\)

DOI10.1016/0377-0427(88)90279-8zbMath0662.30004OpenAlexW2343110159MaRDI QIDQ1113311

John Gill

Publication date: 1988

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(88)90279-8

zbMATH Keywords

attractive fixed pointslimit periodic iteration

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Continued fractions; complex-analytic aspects (30B70)

Related Items (16)

Generalized iteration ⋮ Complex dynamics of the limit periodic system \(F_ n(z)=F_{n-1}(f_ n(z))\), \(f_ n\to f\) ⋮ Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces ⋮ A convergence question inspired by Stieltjes and by value sets in continued fraction theory ⋮ A note on forward iteration of inner functions ⋮ Random holomorphic iterations and degenerate subdomains of the unit disk ⋮ Truncation error bounds for the composition of limit-periodic linear fractional transformations ⋮ Semi-groups of analytic functions that contain the identity map ⋮ Truncation error bounds for the composition of limit-periodic linear fractional transformations ⋮ Stability of the Denjoy-Wolff theorem ⋮ Boundary points as limit functions of iterated holomorphic function systems ⋮ Compositions of contractions ⋮ Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces ⋮ Repeated compositions of analytic maps ⋮ Semi-groups of analytic maps ⋮ Random iterations of holomorphic maps in complex Banach spaces

Cites Work

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• Accelerating convergence of limit periodic continued fractions \(K(a_n/1)\)
• A note on fixed-point continued fractions and Aitken's \(\Delta ^ 2\)- method
• The Use of Attractive Fixed Points in Accelerating the Convergence of Limit-Periodic Continued Fractions
• On convergence of sequences of linear fractional transformations

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