Local Convergence of a multi-point family of high order methods in Banach spaces under H$\ddot{o}$lder continuous derivative Ioannis K. Argyros, Santhosh George

# Local Convergence of a multi-point family of high order methods in Banach spaces under H$\ddot{o}$lder continuous derivativeIoannis K. Argyros, Santhosh George

Abstract:  We present a local convergence analysis for a multi-point family of high order methods in order to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under H$\ddot{o}$lder continuity conditions. Numerical examples are also provided in this study.

Keywords: Multi-point methods, Banach space, Convergence ball, local convergence, H$\ddot{o}$lder continuity.

Ioannis K. Argyros and Santhosh George, Local Convergence of a multi-point family of high order methods in Banach spaces under H$\ddot{o}$lder continuous derivative,  International Journal of Advances in Mathematics, Volume 2018, Number 2, Pages 53-60, 2018.