On relationship between convergence ball of Euler iteration in Banach spaces and its dynamical behavior on Riemann spheres

摘要

The relationship between the convergence ball of the Euler iteration in Banach Spaces and itsexclusive fixed points on Riemann spheres is investigated. By using an exclusive fixed point of the Euleriteration, the convergence ball is determined accurately for a class of operators whose derivatives satisfy somegeneralized Lipschitz condition on Banach spaces.