East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON THE CONVERGENCE OF INEXACT TWO-STEP NEWTON-TYPE METHODS USING RECURRENT FUNCTIONS

  • Argyros, Ioannis K. (Department of Mathematics Sciences Cameron University) ;
  • Hilou, Said (Laboratoire de Mathematiques et Application Poitiers University)
  • Received : 2011.03.02
  • Accepted : 2011.05.04
  • Published : 2011.05.31
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Abstract

We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

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References

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