Taiwanese Journal of Mathematics

SOME NEW ITERATIVE ALGORITHMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS WITH STRICT PSEUDO-CONTRACTIONS AND MONOTONE MAPPINGS

Jian-Wen Peng and Jen-Chih Yao

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Abstract

In this paper, we propose some parallel and cyclic algorithms based on the extragradient method (nonextragradient method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of a finite family of strict pseudo-contractions and the set of the variational inequality for a monotone, Lipschitz continuous mapping (an inverse strongly monotone mapping). We obtain some weak and strong convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, improve and unify some well-known results in the literature.

Article information

Source
Taiwanese J. Math., Volume 13, Number 5 (2009), 1537-1582.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405558

Digital Object Identifier
doi:10.11650/twjm/1500405558

Mathematical Reviews number (MathSciNet)
MR2554475

Zentralblatt MATH identifier
1193.47068

Subjects
Primary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
generalized mixed equilibrium problem extragradient method parallel algorithms cyclic algorithms strict pseudo-contraction monotone mapping

Citation

Peng, Jian-Wen; Yao, Jen-Chih. SOME NEW ITERATIVE ALGORITHMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS WITH STRICT PSEUDO-CONTRACTIONS AND MONOTONE MAPPINGS. Taiwanese J. Math. 13 (2009), no. 5, 1537--1582. doi:10.11650/twjm/1500405558. https://projecteuclid.org/euclid.twjm/1500405558


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References

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