A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces
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Author list: Petrot N., Wattanawitoon K., Kumam P.
Publisher: Elsevier
Publication year: 2010
Journal: Nonlinear Analysis: Hybrid Systems (1751-570X)
Volume number: 4
Issue number: 4
Start page: 631
End page: 643
Number of pages: 13
ISSN: 1751-570X
eISSN: 1878-7460
Languages: English-Great Britain (EN-GB)
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Abstract
We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi-ุ-nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish strong convergence theorems for this algorithm which are connected with results by Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Analysis 70 (2009) 45-57], Qin et al. [X. Qin, Y.J. Cho, S.M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20-30], Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Analysis: Hybrid Systems 3 (2009) 11-20], and many others. ฉ 2010 Elsevier Ltd.
Keywords
Hybrid projection iterative scheme, Quasi-ุ-nonexpansive mapping, Relatively nonexpansive mapping
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