Convergence theorems of shrinking projection methods for equilibrium problem, variational inequality problem and a finite family of relatively quasi-nonexpansive mappings

2011 ◽  
Vol 217 (24) ◽  
pp. 10256-10266 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Jing Zhao
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Variational Inequality Problem ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Finite Family ◽  
Convergence Theorems ◽  
Inequality Problem ◽  
Shrinking Projection Methods

scholarly journals An Iterative Method for a Common Solution of a Combination of the Split Equilibrium Problem, a Finite Family of Nonexpansive Mapping and a Combination of Variational Inequality Problem

2021 ◽  
Vol 52 ◽  
Author(s):  
Ihssane Hay ◽  
Abdellah Bnouhachem ◽  
Themistocles M. Rassias
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Convergence Result ◽  
Finite Family ◽  
Split Equilibrium Problem ◽  
Inequality Problem ◽  
Common Solution

The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.

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