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

Authors

  • Satit Saejung Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
  • Weerayuth Nilsrakoo Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, 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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Journal title

volume 38  issue 4

pages  1047- 1061

publication date 2012-12-15

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