Taiwanese Journal of Mathematics

WEAK CONVERGENCE THEOREM BY A MODIFIED EXTRAGRADIENT METHOD FOR NONEXPANSIVE MAPPINGS AND MONOTONE MAPPINGS

L. C. Ceng, S. Huang, and A. Petrus¸el

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Abstract

In this paper, we introduce a modified extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous mapping. Our modified extragradient method is a variant of the so-called extragradient method. We obtain a weak convergent theorem for two sequences generated by this modified extragradient method.

Article information

Source
Taiwanese J. Math., Volume 13, Number 1 (2009), 225-238.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405280

Digital Object Identifier
doi:10.11650/twjm/1500405280

Mathematical Reviews number (MathSciNet)
MR2489315

Zentralblatt MATH identifier
1169.49005

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 90C29: Multi-objective and goal programming 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
modified extragradient method fixed points monotone mapping nonexpansive mapping variational inequality

Citation

Ceng, L. C.; Huang, S.; Petrus¸el, A. WEAK CONVERGENCE THEOREM BY A MODIFIED EXTRAGRADIENT METHOD FOR NONEXPANSIVE MAPPINGS AND MONOTONE MAPPINGS. Taiwanese J. Math. 13 (2009), no. 1, 225--238. doi:10.11650/twjm/1500405280. https://projecteuclid.org/euclid.twjm/1500405280


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References

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