A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping
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Publication Details
Author list: Kumam P.
Publisher: Springer
Publication year: 2009
Journal: Journal of Applied Mathematics and Computing (1598-5865)
Volume number: 29
Issue number: #
Start page: 263
End page: 280
Number of pages: 18
ISSN: 1598-5865
eISSN: 1865-2085
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, we introduce an iterative scheme by a new hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under some parametric controlling conditions by the new hybrid method which is introduced by Takahashi et al. (J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2007.09.062 , 2007). The results are connected with Tada and Takahashi's result [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mappings and an equilibrium problem, J. Optim. Theory Appl. 133, 359-370, 2007]. Moreover, our result is applicable to a wide class of mappings.
Keywords
Equilibrium problem, Monotone mapping, Nonexpansive mapping, Variational inequality
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