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Extended Convergence of Three Step Iterative Methods for Solving Equations in Banach Space with Applications

Symmetries are vital in the study of physical phenomena such as quantum physics and the micro-world, among others. Then, these phenomena reduce to solving nonlinear equations in abstract spaces. These equations in turn are mostly solved iteratively. That is why the objective of this paper was to obtain a uniform way to study three-step iterative methods to solve equations defined on Banach spaces. The convergence is established by using information appearing in these methods. This is in contrast to earlier works which relied on derivatives of the higher order to establish the convergence. The numerical example completes this paper.