scholarly journals Strong convergence by a hybrid algorithm for solving generalized mixed equilibrium problems and fixed point problems of a Lipschitz pseudo-contraction in Hilbert spaces

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Kasamsuk Ungchittrakool ◽  
Apisit Jarernsuk
2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Kasamsuk Ungchittrakool

We provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed andϕ-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (K). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.


Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1021-1030
Author(s):  
Baohua Guo ◽  
Lijuan Sun

The purpose of this paper is to investigate variational inequalities, fixed point problems and generalized mixed equilibrium problems. Anextragradient iterative algorithm is investigated in the framework of Hilbert spaces. Weak convergence theorems for common solutions are established.


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