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    STUDIA MATHEMATICA - Issue no. 2 / 2014  
         
  Article:   ITERATIVE REGULARIZATION METHODS FOR ILL-POSED HAMMERSTEIN-TYPE OPERATOR EQUATIONS IN HILBERT SCALES.

Authors:  .
 
       
         
  Abstract:  In this paper we report on a method for regularizing a nonlinear Hammerstein type operator equation in Hilbert scales. The proposed method is a combination of Lavrentieve regularization method and a Modi fied Newton`s method in Hilbert scales. Under the assumptions that the operator F is continuously di fferentiable with a Lipschitz-continuous fi rst derivative and that the solution of (1.1) ful fills a general source condition, we give an optimal order convergence rate result with respect to the general source function.

Mathematics Subject Classi fication (2010): 65J20, 65J10, 65R30, 47A52.
Keywords: Nonlinear ill-posed Hammerstein type equations, iterative regularization, adaptive choice, Hilbert scales.
 
         
     
         
         
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