BALL CONVERGENCE RESULTS FOR A METHOD WITH MEMORY OF EFFICIENCY INDEX 1.8392 USING ONLY FUNCTIONAL VALUES

Authors

  • I. Argyros Department of Mathematical Sciences, Cameron University, 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 for an one-step iterative method with memory of efficiency index 1.8392 to solve nonlinear equations. If the function is twice differentiable, then it was shown that the $R-$order of convergence is 1.8392. In this paper we use hypotheses up to the first derivative. This way we extend the applicability of this method. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented to illustrate the theoretical results.

Author Biographies

I. Argyros, Department of Mathematical Sciences, Cameron University, 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,

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Published

2018-01-19

How to Cite

Argyros, I., & George, S. (2018). BALL CONVERGENCE RESULTS FOR A METHOD WITH MEMORY OF EFFICIENCY INDEX 1.8392 USING ONLY FUNCTIONAL VALUES. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 7(2), 91-96. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/400

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Section

Research Article

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