A class of quasi-Newton generalized Steffensen methods on Banach spaces

We consider a class of generalized Steffensen iterations procedure for solving nonlinear equations on Banach spaces without any derivative. We establish the convergence under the Kantarovich–Ostrowskiʹs conditions. The majorizing sequence will be a Newtonʹs type sequence, thus the convergence can have better properties. Finally, a numerical comparation with the classical methods is presented.