A correction note on "Three-step iterative methods for nonlinear equations" and generalization of method
For researchers using iterative methods for nonlinear equations, this correction fixes a theoretical error and offers a generalized method.
The paper corrects errors in a previously published three-step iterative method for nonlinear equations, showing that the original proof of cubic convergence was flawed, and provides a corrected derivation and generalization.
In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated a theorem (\textbf{Theorem 2.3}) to prove the cubic order of convergence but the given proof does not show cubic order of convergence. Actually, the mathematical derivation steps to develop the \textbf{Algorithm 2.3} are wrong. In this note, we present the correct mathematical developments and finally provide computational order of convergence in the favor of our claim and provide the generalization of the method.