An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

L. C. Ceng; S. Al-Homidan; Q. H. Ansari; J. C. Yao

doi:10.1016/j.cam.2008.03.032

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

L. C. Ceng, S. Al-Homidan, Q. H. Ansari^*, J. C. Yao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

136 Scopus citations

Abstract

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu's result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-346], and Takahashi and Takahashi's result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

Original language	English
Pages (from-to)	967-974
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	223
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2008.03.032
State	Published - 15 Jan 2009

Bibliographical note

Funding Information:
In this research, first author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai, second and third authors were supported by a KFUPM Funded Research Project No. # IN070362 and fourth author was partially supported by a grant from the National Science Council of Taiwan.

Keywords

Bifunctions
Demiclosedness
Equilibrium problem
Fixed points
Iterative scheme
Strict pseudo-contraction mappings

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2008.03.032

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title = "An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings",

abstract = "In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu's result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-346], and Takahashi and Takahashi's result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.",

keywords = "Bifunctions, Demiclosedness, Equilibrium problem, Fixed points, Iterative scheme, Strict pseudo-contraction mappings",

author = "Ceng, \{L. C.\} and S. Al-Homidan and Ansari, \{Q. H.\} and Yao, \{J. C.\}",

note = "Funding Information: In this research, first author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai, second and third authors were supported by a KFUPM Funded Research Project No. \# IN070362 and fourth author was partially supported by a grant from the National Science Council of Taiwan.",

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doi = "10.1016/j.cam.2008.03.032",

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AU - Ceng, L. C.

AU - Al-Homidan, S.

AU - Ansari, Q. H.

AU - Yao, J. C.

N1 - Funding Information: In this research, first author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai, second and third authors were supported by a KFUPM Funded Research Project No. # IN070362 and fourth author was partially supported by a grant from the National Science Council of Taiwan.

PY - 2009/1/15

Y1 - 2009/1/15

N2 - In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu's result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-346], and Takahashi and Takahashi's result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

AB - In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu's result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-346], and Takahashi and Takahashi's result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

KW - Bifunctions

KW - Demiclosedness

KW - Equilibrium problem

KW - Fixed points

KW - Iterative scheme

KW - Strict pseudo-contraction mappings

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DO - 10.1016/j.cam.2008.03.032

M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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