On Sn Iteration for Fixed Points of (E)-Operators with Numerical Analysis and Polynomiography

The first part of this study is related to the search of fixed points for (E)-operators (Garcia-Falset operators), in the Banach setting, by means of a three-step iteration procedure. The main results reveal some conclusions related to weak and strong convergence of the considered iterative scheme toward a fixed point. On the other hand, the usefulness of the Sn iterative scheme is once again revealed by demonstrating through numerical simulations the advantages of using it for solving the problem of the maximum modulus of complex polynomials compared to standard algorithms, such as Newton, Halley, or Kalantary’s so-called B4 iteration.