Journal
FIXED POINT THEORY AND APPLICATIONS
Volume -, Issue -, Pages 1-17Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/1687-1812-2012-65
Keywords
strict pseudo-contractions; variational inequality; strong convergence theorem; q-uniformly smooth Banach space; common fixed point
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Funding
- Centre of Excellence in Mathematics under the Commission on Higher Education, Thailand [RG-1-54-02-1]
- Centre of Excellence in Mathematics
- Commission on High Education, Thailand at King Mongkut's University of Technology Thonburi (KMUTT)
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In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized duality mapping. The results presented in this article extend and generalize the corresponding results announced by Yamada and Ceng et al. from Hilbert spaces to Banach spaces.
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