Communications of the
Korean Mathematical Society CKMS

The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al.~using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.

Keywords: Banach space, Newton's method, semi-local convergence, order of convergence, efficiency index

MSC numbers: 65H10, 65J15, 65G99, 47J25