ABSTRACT
We study perturbations of a hybrid steepest descent method for locating common fixed points of an arbitrary pool of nonexpansive mappings. The difficulty of handling a possibly uncountable family is settled down to dealing with a countable family of auxiliary mappings
associated to
, in the sense that the approximate fixed points of
provide the common fixed points of
. Algorithms with strong convergence for solving the associated variational inequality problems are presented. Applications to convex minimization problems and convex feasibility problems are provided, together with numerical examples for comparisons of our algorithms with the existing ones.
Acknowledgments
We would like to express our deep gratitude to the referees for many useful ideas and suggestions to improve the paper.
This work is supported by Taiwan MOST grants 105-2115-M-039-002-MY3 (for Yao) and 108-2115-M-110-004-MY2 (for Wong).
Authors' contributions
All authors contribute equally and significantly in writing this paper. All readers read and approved the final manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.