Semilocal Convergence Theorem for the Secant Method under Mysovskii-type Condition

The Mysovskii-type condition is considered in this study for the secant method in Banach spaces for solving a nonlinear operator equation. It is assumed that the divided difference of order one is Hlder continuous and its inverse is bounded. A semilocal convergence theorem is established, and a error estimate formula is given. Finally, an example is provided to show the application of our theorem.