A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping
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Author list: Kumam P.
Publisher: Elsevier
Publication year: 2008
Journal: Nonlinear Analysis: Hybrid Systems (1751-570X)
Volume number: 2
Issue number: 4
Start page: 1245
End page: 1255
Number of pages: 11
ISSN: 1751-570X
eISSN: 1878-7460
Languages: English-Great Britain (EN-GB)
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Abstract
The purpose of this paper is to present an iterative scheme by a 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 the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. © 2008 Elsevier Ltd. All rights reserved.
Keywords
Hybrid method
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