scholarly journals Iterative methods for mixed equilibrium problems and strictly pseudocontractive mappings

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Jong Soo Jung
Keyword(s):  
Iterative Methods ◽  
Equilibrium Problems ◽  
Pseudocontractive Mappings ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
Strictly Pseudocontractive Mappings

scholarly journals A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Poom Kumam ◽  
Phayap Katchang
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
General System ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Pseudocontractive Mappings ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
Strictly Pseudocontractive Mappings

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others.

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