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

Document Type: Research Paper

Authors

1 Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand

2 Department 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.

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Main Subjects