Convergence of the Ulm-like method under the hölder condition

In this paper, we study the convergence problem of an Ulm-like method for solving nonlinear operator equations without computing (approximate) Jacobian matrices and solving (approximate) Jacobian equations. Under the assumption that the first Frechet derivative satisfies the Holder condition, the Ulm-like method yields superlinear convergence. A numerical example is provided to demonstrate the efficacy of our convergence analysis.