Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems

2013 ◽  
Vol 57 (4) ◽  
pp. 1299-1318 ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam ◽  
Yeol Je Cho
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators

scholarly journals Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zi-Ming Wang ◽  
Poom Kumam
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Projection Algorithm ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Convex Feasibility ◽  
Hybrid Projection Algorithm

Two countable families of hemirelatively nonexpansive mappings are considered based on a hybrid projection algorithm. Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied.

scholarly journals Strong Convergence Theorems for Maximal Monotone Operators, Fixed-Point Problems, and Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng ◽  
De-ning Qu
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Element ◽  
Convergence Theorems ◽  
New Iterative Method

We present a new iterative method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions to an equilibrium problem, and the set of zeros of the sum of maximal monotone operators and prove the strong convergence theorems in the Hilbert spaces. We also apply our results to variational inequality and optimization problems.

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