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Iterative Methods in Metric Spaces

In: Approximate Solutions of Common Fixed-Point Problems

Author

Listed:
  • Alexander J. Zaslavski

    (The Technion - Israel Institute of Technology)

Abstract

In this chapter we study the convergence of iterative methods for solving common fixed point problems in a metric space. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that the iterative method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.

Suggested Citation

  • Alexander J. Zaslavski, 2016. "Iterative Methods in Metric Spaces," Springer Optimization and Its Applications, in: Approximate Solutions of Common Fixed-Point Problems, chapter 0, pages 49-97, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-33255-0_3
    DOI: 10.1007/978-3-319-33255-0_3
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