scholarly journals WEAK CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, MONOTONE MAPPINGS AND PSEUDOCONTRACTIVE MAPPINGS

2015 ◽  
Vol 52 (6) ◽  
pp. 1179-1194
Author(s):  
JONG SOO JUNG
Keyword(s):  
Weak Convergence ◽  
Equilibrium Problems ◽  
Monotone Mappings ◽  
Convergence Theorems ◽  
Generalized Mixed Equilibrium Problems ◽  
Pseudocontractive Mappings ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

scholarly journals Extragradient algorithms for variational inequality, fixed point and generalized mixed equilibrium problems

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1021-1030
Author(s):  
Baohua Guo ◽  
Lijuan Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

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.

scholarly journals Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Poom Kumam ◽  
Usa Hamphries ◽  
Phayap Katchang
Keyword(s):  
Fixed Points ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Common Element ◽  
Monotone Mappings ◽  
Generalized Mixed Equilibrium Problems ◽  
Pseudocontractive Mappings ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Strictly Pseudocontractive Mappings

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors.

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