Newton–Kantorovich theorem for a family of modified Halley’s method under Hölder continuity conditions in Banach space

In this study, under pp-Hölder continuity conditions a family of new modified Halley’s method with (2 + p)-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 modified Halley’s method is established under Hölder continuity conditions. The error estimate also is gotten. Finally, two examples are provided to show the application of our theorem.