Algorithms for solving generalized equilibrium problems and fixed points of nonexpansive semigroups in Hilbert spaces

Optimization ◽  
2012 ◽  
Vol 63 (5) ◽  
pp. 799-815 ◽  
Author(s):  
Suthep Suantai ◽  
Prasit Cholamjiak
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Semigroups ◽  
Generalized Equilibrium

scholarly journals Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Nimit Nimana
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Shrinking Projection Method ◽  
Generalized Equilibrium

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.

scholarly journals Approximation of fixed points for nonexpansive semigroups in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
pp. 31 ◽  
Author(s):  
Yonghong Yao ◽  
Jung Kang ◽  
Yeol Cho ◽  
Yeong-Cheng Liou
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Semigroups

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate 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 Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Fixed Points and Existence Theorems of Maximal Elements with Applications in FC-Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Rong-Hua He
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Maximal Elements ◽  
Minimax Theory ◽  
Coincidence Theorems ◽  
Generalized Equilibrium

We present some fixed point theorems and existence theorems of maximal elements in FC-space from which we derive several coincidence theorems. Applications of these results to generalized equilibrium problems and minimax theory will be given. Our results improve and generalize some recent results.

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