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.
Nonlinear equations Order of convergence Iterative methods Semilocal convergence Hammerstein equation
Hueso, J.L., Martínez, E., Torregrosa, J.R.: Third and fourth order iterative methods free from second derivative for nonlinear systems. Appl. Math. Comput. 211, 190–197 (2009)MathSciNetCrossRefMATHGoogle Scholar
Hueso, J.L., Martínez, E.: Semilocal convergence of a family of iterative methods in Banach spaces. Numer. Algor. In Press. doi:10.1007/s11075-013-9795-7