Semilocal Convergence Domain of a Chandrasekhar Integral Equation

In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines the domain of convergence under appropriate initial estimates. In addition, the uniqueness domain for the solution and the error bounds are obtained. Next, several numerical examples, one which includes a Chandrasekhar integral equation, are carried out to apply the theoretical findings for semilocal convergence. Then, a final overview is provided.