Analysis of semilocal convergence under W-continuity condition on second order Frechet derivative in Banach space

Abstract

This article proposed the study of semilocal convergence of multi-step Newton's type approach in Banach spaces using recurrence relation technique. It is realized that the w- continuity condition is a generalization of the Lipschitz condition. The existence and uniqueness theorem has been formed, which validate the substantiate of our approach. Finally, a numerical example has been presented to vindicate the theoretical results.