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DOI: 10.23952/jnfa.2024.20
Received August 1, 2024; Accepted September 11, 2024; Published October 3, 2024
Abstract. The objective of this paper is two-fold. First, the essential characteristics of the iterative methods of fixed point approximation are extracted, and the convergence of sequences not linked to particular algorithms are studied. The second aim of this paper is to present a new three-steps iterative procedure. The convergence of the procedure for the approximation of fixed points of partial contractivities and nonexpansive partial contractivities is analyzed. In the nonexpansive case, the results of weak and strong convergence of the method are given when the underlying spaces are Banach and enjoy some properties, such as uniform convexity or Opial condition.
How to Cite this Article:
M.A. Navascués, Approximation sequences for fixed points of non contractive operators, J. Nonlinear Funct. Anal. 2024 (2024) 20.