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
Article
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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.

Keywords

Banach Space Lipschitz Condition Nonlinear Operator Local Convergence Convergence Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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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