대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권4호
  • /
  • Pages.781-793
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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LOCAL CONVERGENCE FOR SOME THIRD-ORDER ITERATIVE METHODS UNDER WEAK CONDITIONS

  • Argyros, Ioannis K. (Department of Mathematical Sciences Cameron University) ;
  • Cho, Yeol Je (Department of Mathematics Education and the RINS Gyeongsang National University, Department of Mathematics King Abdulaziz University) ;
  • George, Santhosh (Department of Mathematical and Computational Sciences NIT)
  • 투고 : 2015.04.18
  • 발행 : 2016.07.01
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초록

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

참고문헌

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피인용 문헌

  1. Ball convergence of some iterative methods for nonlinear equations in Banach space under weak conditions 2017, https://doi.org/10.1007/s13398-017-0420-9
  2. Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions vol.54, pp.2, 2016, https://doi.org/10.1515/awutm-2016-0013
  3. Local Convergence for a Frozen Family of Steffensen-Like Methods under Weak Conditions vol.1, 2017, https://doi.org/10.11131/2017/101259