An improved semi-local convergence analysis for a three point method of order 1.839 in banach space

Abstract

We present a new semi-local convergence analysis for a three point method of order 1.839 in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of the new approach over earlier ones such as [18] are: weaker and easier to verify convergence conditions. Moreover the radius of convergence is given in an explicit form. Furthermore, uniqueness results are also presented for the first time as far as we know in this paper. Finally, numerical example illustrating the theoretical results is given.