Abstract
In order to estimate the solution of the zero for the nonlinear systems, we conduct the local convergence investigation in this paper. In contrast to the Lipschitz condition used in the preceding study, we have used the Hölder continuity requirement. Additionally, we use a derivative approximation to take the derivative free iterative technique with the same order. A computed radius of convergence balls based on the Hölder constant is also provided. No Taylor's series approximation on a higher order Fréchet derivate is used in this investigation. To broaden the relevance of our work, a comparison of convergence ball radii is also provided. This highlights the uniqueness of this paper.
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