A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping |
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Authors: | Poom Kumam |
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Institution: | aDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bang Mod, Bangkok 10140, Thailand |
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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. |
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Keywords: | Hybrid method Nonexpansive mapping Equilibrium problem Variational inequality Monotone mapping |
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