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Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

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  • Yonghui Ling
  • Xiubin Xu
  • Shaohua Yu

Abstract

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.

Suggested Citation

  • Yonghui Ling & Xiubin Xu & Shaohua Yu, 2013. "Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jnlaaa:682167
    DOI: 10.1155/2013/682167
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