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

Authors

  • IOANNIS K. ARGYROS Ioannis K. Argyros, Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA
  • SANTHOSH GEORGE Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Keywords:

Jarratt-type methods, Banach space, Local Convergence, Frechet-derivative

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

IOANNIS K. 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

SANTHOSH 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

Additional Files

Published

11/28/2016

Issue

Vol. 6 No. 2 (2015): JNAO

Section

Research Articles

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Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.