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Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

Article 14, Volume 38, Number 4, December 2012, Page 1047-1061  XML PDF (342 K)
Document Type: Research Paper
Authors
1Weerayuth Nilsrakoo ; 2Satit Saejung
1Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand
2Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
Abstract
We prove a strong convergence result for a sequence generated by
Halpern's type iteration for approximating a common fixed point of a
countable family of quasi-Lipschitzian mappings in a real Hilbert
space. Consequently, we apply our results to the problem of finding
a common fixed point of asymptotically nonexpansive mappings, an
equilibrium problem, and a variational inequality problem for
continuous monotone mappings.
Keywords
Asymptotically nonexpansive mapping; equilibrium problem; quasi-Lipschitzian mapping; strong convergence theorem; variational inequality problem
Main Subjects
46-XX Functional Analysis; 47-XX Operator theory
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