A one parameter square root family of two-step root-finders

A one parameter family of iterative methods for solving nonlinear equations is constructed. All the methods of the proposed family are cubically convergent for a simple root, except one particular method which attains the fourth order without the increase of computational cost. These methods belong to the class of two-step methods and require three function evaluations per iteration. The square-root structure of the family provides finding a complex zero of real functions in some cases. A comparison analysis shows that the presented family generates the methods which are comparable or even superior than the existing two-step iterative methods of the third order.