Convergence analysis for a family of improved super-Halley methods under general convergence condition (Q2248967)

The authors study the semilocal convergence of a family of improved super-Halley methods for solving nonlinear operator equations in Banach spaces. They use recurrence relations to prove the convergence assuming a general continuity condition on the third-order Fréchet derivative of the involved operator. This approach allows them to show in addition an existence-uniqueness result for the nonlinear equation. An application to the solution of nonlinear integral equations is also given.