Abstract

We apply a string-averaging algorithm for common fixed point problems with a countable family of quasi-nonexpansive operators in an arbitrary normed space and show its convergence. Our results are an extension of the recent results by T. Y. Kong, H. Pajoohesh and G. T. Herman obtained for operators which are projections on convex closed sets in a finite-dimensional Euclidean space.

Author information

Contact details are reproduced from the original publication and may be historical.

Alexander J. Zaslavski

Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel

ajzasl@technion.ac.il

Keywords

  • Convergence analysis
  • fixed point
  • inexact iterate
  • normed space
  • nonexpansive mapping

Mathematics Subject Classification

47H04, 47H09, 47H10

Suggested citation

A. J. Zaslavski. “Convergence of the String-Averaging Algorithm for Common Fixed Point Problems with a Countable Family of Operators.” Journal of Convex Analysis 32 (2025), No. 4, 1065–1082. https://doi.org/10.68381/jca32056

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press.