Extended iterative schemes based on decomposition for nonlinear models

We suggest the local analysis of a class of iterative schemes based on decomposition technique for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the fourth derivative to establish convergence. But we only apply the first derivative in our convergence theorem. We also provide computable radius of convergence ball, error estimates and uniqueness of the solution results not studied in earlier works. Hence, we enhance the applicability of these schemes. Furthermore, we explore, using basin of attraction tool, the dynamics of the schemes when they are applied on various complex polynomials. This article is concluded with numerical experiments.