Extended Local Convergence for the Chebyshev Method under the Majorant Condition

In this article, we present the study on local convergence behaviour of Chebyshev's method, which is a third order iterative method used to solve a non-linear system in Banach space locale. In contrast to the earlier works, we establish the convergence using restricted-majorant conditions. As a result, we get betterconvergence radius and more tighter error estimates in comparison to the previous researches. Suitable numerical examples complement the theory.