Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CONVERGENCE OF A CONTINUATION METHOD UNDER MAJORANT CONDITIONS

  • Nisha, Shwet (Department of Mathematics Central University of Jharkhand) ;
  • Parida, P.K. (Department of Mathematics Central University of Jharkhand) ;
  • Kumari, Chandni (Department of Mathematics Central University of Jharkhand)
  • Received : 2019.06.12
  • Accepted : 2019.09.30
  • Published : 2019.12.30
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Abstract

The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.

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References

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