Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations

From well-known secant-like methods, we observe that we can construct a new family of secant-like methods that includes the secant method and Kurchatov's method. We analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators. Finally, we apply our results to conservative problems.