Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems

In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the...

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Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 32; no. 2
Main Authors Jaiboon, C, Kumam, P, Humphries, U W
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2009
Subjects
Mathematics
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ISSN0126-6705
2180-4206

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Abstract In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi [7]. 2000 Mathematics Subject Classification: 47H09, 47H10, 49J40, 47J20.
AbstractList In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi [7]. 2000 Mathematics Subject Classification: 47H09, 47H10, 49J40, 47J20.
Author Humphries, U W
Jaiboon, C
Kumam, P
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