scholarly journals An iterative algorithm to approximate a common element of the set of common fixed points for a finite family of strict pseudo-contractions and of the set of solutions for a modified system of variational inequalities

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Atid Kangtunyakarn
Keyword(s):  
Variational Inequalities ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Common Fixed Points ◽  
Finite Family ◽  
Common Element ◽  
System Of Variational Inequalities

scholarly journals Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian-Fen Gong ◽  
Dao-Jun Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Common Fixed Points ◽  
Finite Family ◽  
Steepest Descent ◽  
Descent Methods ◽  
Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.

scholarly journals A viscosity iterative algorithm for the optimization problem system

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2249-2266 ◽  
Author(s):  
H.R. Sahebi ◽  
S. Ebrahimi
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Optimization Problem ◽  
Common Fixed Points ◽  
Numerical Results ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Mixed Equilibrium Problem

In this paper, we suggest and analysis a viscosity iterative algorithm for finding a common element of the set of solution of a mixed equilibrium problem and the set the of solutions of a variational inequality and all common fixed points of a nonexpansive semigroup. This algorithm strongly converges to an element which solves an optimization problem system. Finally, some examples and numerical results are also given.

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