An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings
By Lu-Chuan Ceng, Suliman S. Al-Homidan, Qamrul Hasan Ansari, Jen-Chih Yao. 2009
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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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/928d7e26e36b04fb0d8eb76c631cb77c10bede63
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Citations in the corpus
- Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces (2010, background): “, [2–9] and the references therein for recent results on existence and iterative schemes.”