# Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations

### Abstract

In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighth

order have been utilized to establish the convergence of a derivative free class of seventh order

iterative algorithms. Moreover, no error distances or results on uniqueness of the solution were

given. In this study, extended ball convergence analysis is derived for this class by imposing

conditions on the first derivative. Additionally, we offer error distances and convergence radius

together with the region of uniqueness for the solution. Therefore, we enlarge the practical

utility of these algorithms. Also, convergence regions of a specific member of this class are displayed

for solving complex polynomial equations. At the end, standard numerical applications

are provided to illustrate the efficacy of our theoretical findings.

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