On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions
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- Hernández-Verón, M.A. & Martínez, E. Numer Algor (2015) 70: 377. doi:10.1007/s11075-014-9952-7
In this paper the semilocal convergence for an alternative to the three steps Newton’s method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.