Super-Halley method under majorant conditions in Banach spaces

Abstract

In this paper, we have studied local convergence of Super-Halley method in Banach spaces under the assumption of second order majorant conditions. This approach allows us to obtain generalization of earlier convergence analysis under majorizing sequences. Two important special cases of the convergence analysis based on the premises of Kantorovich and Smale type conditions have also been concluded. To show efficacy of our approach we have given three numerical examples.

Keywords

• nonlinear equations
• super-halley method
• majorant conditions
• local convergence
• semilocal convergence
• smale-type conditions
• kantorovich-type conditions