In this paper, we introduce a new iteration process and prove the convergence of this iteration process to a fixed point of contractive-like operators. We also present a data dependence result for such mappings. Our results unify and extend various results in the existing literature.

The aim of this paper is to show that Newton-like S-iteration method converges to the unique solution of the scalar nonlinear equation f(x) = 0 under weaker conditions involving only f and f 0. We also present numerical examples to support our analytical results.