A note on a modification of Moser's method

We use a recurrence technique to obtain semilocal convergence results for Ulm's iterative method to approximate a solution of a nonlinear equation F(x)=0F(x)=0xn+1=xn-BnF(xn),n≥0,Bn+1=2Bn-BnF′(xn+1)Bn,n≥0.This method does not contain inverse operators in its expression and we prove it converges with the Newton rate. We also use this method to approximate a solution of integral equations of Fredholm-type.