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On relationship between convergence ball of Euler iteration in Banach spaces and its dynamical behavior on Riemann spheres. (English) Zbl 1217.37045
Summary: The relationship between the convergence ball of the Euler iteration in Banach Spaces and its exclusive fixed points on Riemann spheres is investigated. By using an exclusive fixed point of the Euler iteration, the convergence ball is determined accurately for a class of operators whose derivatives satisfy some generalized Lipschitz condition on Banach spaces.
MSC:
37F10Polynomials; rational maps; entire and meromorphic functions
37N30Dynamical systems in numerical analysis
30H05Bounded analytic functions
47J25Iterative procedures (nonlinear operator equations)