LOCAL CONVERGENCE OF A MULTI-POINT JARRATT-TYPE METHOD IN BANACH SPACE UNDER WEAK CONDITIONS

Authors

  • I. Argyros Ioannis K. 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 local convergence analysis of a multi-point Jarratt-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fr\'{e}chet-derivative of the operator involved. In contrast to earlier studies using hypotheses up to the third Fr\'{e}chet-derivative [26]. Numerical examples are also provided in this study.

Author Biographies

I. Argyros, Ioannis K. Argyros, Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA

Professor, Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

S. George, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Professor, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

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Published

2016-11-28

How to Cite

Argyros, I., & George, S. (2016). LOCAL CONVERGENCE OF A MULTI-POINT JARRATT-TYPE METHOD IN BANACH SPACE UNDER WEAK CONDITIONS. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 6(2), 43-52. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/353

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Section

Research Article

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