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Infinite Products

  • Simeon Reich
  • Alexander J. Zaslavski
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 34)

Abstract

Chapter 6 is devoted to the study of convergence of infinite products of different classes of mappings. The convergence of infinite products of nonexpansive mappings is of major importance because of their many applications in the study of feasibility and optimization problems. We study the convergence of typical (generic) infinite products of mappings to the set of their common fixed points, and establish weak ergodic theorems (a term which originates in population biology), which roughly mean that all trajectories generated by infinite products converge to each other. We study convergence and its stability for generic infinite products of nonexpansive mappings, uniformly continuous mappings, order-preserving mappings, order-preserving linear mappings, homogeneous order-preserving mappings, products of affine mappings, as well as products of resolvents of accretive operators.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Simeon Reich
    • 1
  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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