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ON THE "TERRA INCOGNITA" FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS

  • Argyros, Ioannis Konstantinos (Department of Mathematics Sciences Cameron University) ;
  • Cho, Yeol Je (Department of Mathematics Education and the RINS Gyeongsang National University) ;
  • George, Santhosh (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka)
  • Received : 2013.02.20
  • Accepted : 2013.08.14
  • Published : 2014.03.01

Abstract

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

Keywords

References

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