On the Convergence Order of Jarratt-Type Methods for Nonlinear Equations

The convergence order of Jarratt-type methods for solving nonlinear equations are obtained without using the Taylor expansion. We use assumptions on the derivatives of the involved operator up to second order only contrary to the earlier studies. The proof provided in this paper does not depend on the Taylor series expansion which in turn reduces assumptions on the higher order derivatives of the involved operator and increases the applicability of these methods. The applicability of the method is further extended using the concept of generalized condition in the local convergence and majorizing sequences in the semi-local analysis. Numerical examples and Basins of attractions of the methods are provided in this study.