Semilocal convergence of a modified Chebyshev-like's method for solving nonlinear equations under generalized weak condition

摘要

In this paper, the semilocal convergence of the modified Chebyshev-like's method is established by using recurrence relations under generalized weak condition. We prove an existence-uniqueness theorem and give a priori error bound which demonstrates the R-order convergence of the method. Moreover, the dynamical behavior of this method is also studied. Finally, numerical examples are presented to demonstrate our approach.