Convergence theorems of a hybrid algorithm for equilibrium problems
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Author list: Kumam P., Wattanawitoon K.
Publisher: Elsevier
Publication year: 2009
Journal: Nonlinear Analysis: Hybrid Systems (1751-570X)
Volume number: 3
Issue number: 4
Start page: 386
End page: 394
Number of pages: 9
ISSN: 1751-570X
eISSN: 1878-7460
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of common fixed points of two hemi-relatively non-expansive mappings and the set of solutions of an equilibrium problem by the CQ hybrid method in Banach spaces. Our results improve and extend the corresponding results announced by Cheng and Tian [Y. Cheng, M. Tian, Strong convergence theorem by monotone hybrid algorithm for equilibrium problems, hemi-relatively nonexpansive mappings and maximal monotone operators, Fixed Point Theory Appl. 2008 (2008) 12 pages, doi:10.1155/2008/617248], Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively non-expansive mappings, Fixed Point Theory Appl. (2008) doi:10.1155/2008/528476] and some others. ฉ 2009 Elsevier Ltd. All rights reserved.
Keywords
Hemi-relatively non-expansive mapping, Monotone hybrid algorithm
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