ON THE SEMILOCAL CONVERGENCE OF A TWO STEP NEWTON METHOD UNDER THE $\GAMMA-$CONDITION

Authors

  • I. Argyros Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA
  • S. George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Abstract

We present a semilocal convergence analysis of a two-step Newton method using the $\alpha-$theory in order to approximate a locally unique solution of an equation in a Banach space setting. The new idea uses a combination of center$-\gamma$ as well as a $\gamma-$ condition in the convergence analysis. This convergence criteria are weaker than the corresponding ones in the literature even in the case of the single step Newton method [3, 14, 15, 16, 17, 18, 19, 20]. Numerical examples involving a nonlinear integral equation where the older convergence criteria are not satisfied but the new convergence criteria are satisfied, are also presented in the paper.

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Published

2016-11-28

How to Cite

Argyros, I., & George, S. (2016). ON THE SEMILOCAL CONVERGENCE OF A TWO STEP NEWTON METHOD UNDER THE $\GAMMA-$CONDITION. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 6(2), 73-84. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/325

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Section

Research Article

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