Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method

In this paper, a family of new deformed Chebyshev method with third-order is proposed in Banach space which is used to solve the nonlinear operator equations. The Newton–Kantorovich convergence theorem for the family of new deformed Chebyshev method is established by using majorizing function. The error estimate is also obtained. Finally, few examples are provided to show the application of our theorems.