Journal
FIXED POINT THEORY AND APPLICATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER INT PUBL AG
DOI: 10.1186/1687-1812-2011-11
Keywords
Banach space; Fixed point; Metric projection; Generalized equilibrium problem; Nonexpansive mapping
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Funding
- Office of the Higher Education Commission, Thailand
- Commission on Higher Education, Ministry of Education, Thailand
- Office of the Higher Education Commission
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We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings.
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