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

Cristian Ciobanescu ()
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Cristian Ciobanescu: Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 16, 1-14

Abstract: 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 S n 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 B 4 iteration.

Keywords: fixed point; ( Eμ ) mapping; convergence analysis; Sn iteration; polynomiography (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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