Local convergence of Super Halley’s method under weaker conditions on Fréchet derivative in Banach spaces

Abstract

Super Halley’s method is one of the most important iterative methods for solving nonlinear equations in Banach spaces. It’s local and semilocal convergence analysis is established using either majorizing sequences or recurrence relations under various continuity conditions such as Lipschitz or Holder using first/second order Frechet derivatives. In this paper, an attempt is made to establish it’s local convergence analysis under weaker continuity conditions on first order Frechet derivative. This work generalizes the earlier work in this direction and it is observed that it is applicable to cases whether they either fail to converge or give smaller balls of convergence.