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.
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.
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