A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

By Meijuan Shang, Yongfu Su, Xiaolong Qin. 2008

125 citations recorded by the source corpus.

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/57d99ebaeded5dfb46438d5d97b1cd7e343f3441

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Mixed equilibrium problems and optimization problems (2009, methodology): “Some methods have been proposed to solve the MEP and EP, see, for example, [5–17,25–31].”
Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings (2011, methodology): “1) based on iterative methods in the framework of real Hilbert spaces; see, for instance [4,6-14] and the references therein.”