Local convergence of efficient Secant-type methods for solving nonlinear equations

A local convergence analysis for an efficient Secant-type method (STM) for solving nonlinear equations is given using both the Lipschitz continuous and center-Lipshchitz continuous divided differences of order one. An estimate of the radius of the convergence ball of (STM) is provided, the error estimate matching its convergence order is established. Numerical examples validating the theoretical results are also provided in the concluding section of this study.