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

Chandni Kumari, Pradip K. Parida

• 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.