Study of semilocal convergence analysis of Chebyshev’s method under new type majorant conditions

In this work, we will present semilocal convergence of Chebyshev’s method for solving nonlinear operator equations in Banach spaces. This method is a third order iterative method. Here, we present a new semilocal convergence analysis for Chebyshev’s method by using a new type of majorant condition. Additionally, we also obtain an error estimate based on a twice directional derivative of the majorizing function. We will also present two important special cases about the convergence result based on the Kantorovich-type and Smale-type assumptions that will show that our results generalizes these earlier convergence results. Two numerical examples are also worked out to show efficiency of our study.