Analysis of semilocal convergence in Banach spaces under relaxed condition and computational efficiency

The present paper is concerned with the study of semilocal convergence of a fifth-order method for solving nonlinear equations in Banach spaces under mild conditions. An existence and uniqueness theorem is proved and followed by error estimates. The computational superiority of the considered scheme over the identical order methods is also examined, which shows the efficiency of the present scheme from a computational point of view. Lastly, an application of the theoretical development is made in a nonlinear integral equation.