On the local convergence of Weerakoon's method under Hölder continuity condition in Banach spaces

Abstract

In this manuscript, the study of local convergence analysis for the cubically convergent Weerakoon’s method using Hölder continuity condition is presented to solve nonlinear equations in Banach spaces. Hölder continuity condition on the first derivative is assumed to extend the applicability of the method on such problems for which Lipschitz condition fails. This convergence analysis generalises the local convergence with Lipschitz continuity condition. A theorem showing existence and uniqueness of the solution with the error bounds is established. To verify our theoretical findings some numerical examples like Hammerstein integral equation and a system of nonlinear equations are solved.