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

作者：Ceng L C; Al Homidan S; Ansari Q H^*; Yao J C

来源：Journal of Computational and Applied Mathematics, 2009, 223(2): 967-974.

DOI：10.1016/j.cam.2008.03.032

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

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.

• 出版日期2009-1-15
• 单位上海师范大学; 中国石油大学（北京）; 中山大学