scholarly journals Relaxed and composite viscosity methods for variational inequalities, fixed points of nonexpansive mappings and zeros of accretive operators

2014 ◽  
Vol 2014 (1) ◽  
pp. 29 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Abdullah Al-Otaibi ◽  
Qamrul Ansari ◽  
Abdul Latif
Keyword(s):  
Variational Inequalities ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Accretive Operators

scholarly journals Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Bashir Ali
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem ◽  
Points Approximation

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results.

scholarly journals Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Luigi Muglia ◽  
Giuseppe Marino
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Unique Solution ◽  
Nonexpansive Mappings ◽  
Multivalued Maps ◽  
Demiclosedness Principle

AbstractMultivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality.

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