Strong Convergence to Common Fixed Points of Countable Relatively Quasi-Nonexpansive Mappings

By Weerayuth Nilsrakoo, Satit Saejung. 2008

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Correspondence should be addressed to Satit Saejung,saejung@kku.ac.thReceived 30 August 2007; Accepted 24 December 2007Recommended by Simeon ReichWe prove that a sequence generated by the monotone CQ-method converges strongly to a commonfixed point of a countable family of relatively quasi-nonexpansive mappings in a uniformly convexand uniformly smooth Banach space. Our result is applicable to a wide class of mappings.Copyrightq2008 W. Nilsrakoo and S. Saejung. This is an open access article distributed underthe Creative Commons Attribution License, which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

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Citations in the corpus

• A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, background): “A mapping T from C into itself is said to be relatively nonexpansive [33–35] if F̂(T ) = F(T ) and φ(p, Tx) ≤ φ(p, x) for all x ∈ C and p ∈ F(T ).”