Journal of Mathematical Sciences

, Volume 168, Issue 4, pp 576–584 | Cite as

On a two-step iterative process under generalized Lipschitz conditions for first-order divided differences

  • S. M. Shakhno

We investigate a Newton-type two-step iterative method, using the approximation of the Fréchet derivative of a nonlinear operator by divided differences. We study the local convergence of this method provided that the first-order divided differences satisfy the generalized Lipschitz conditions. The conditions and rate of convergence of this method are determined, and the domain of uniqueness of solution of the equation is found.


Banach Space Lipschitz Condition Nonlinear Operator Local Convergence Convergence Order 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • S. M. Shakhno
    • 1
  1. 1.Franko Lviv National UniversityLvivUkraine

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