A family of modified super-Halley methods with fourth-order convergence

In this paper, we present a family of modified super-Halley methods for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. The superiority of the new methods is that they require no additional evaluations of the function, the first derivative or second derivative as compared with the classical third-order methods although their order is improved. Numerical results show that the new methods can be efficient.