scholarly journals Pseudomonotone variational inequalities and fixed points

2021 ◽  
Vol 22 (2) ◽  
pp. 543-558
Author(s):  
L.C. Ceng ◽  
◽  
A. Petrușel ◽  
X. Qin ◽  
J.C. Yao ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Fixed Points

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

scholarly journals Approximation for the Hierarchical Constrained Variational Inequalities over the Fixed Points of Nonexpansive Semigroups

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-Jun Zhu
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Linear Operators ◽  
Nonexpansive Semigroup ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Nonexpansive Semigroups

The purpose of the present paper is to study the hierarchical constrained variational inequalities of finding a pointx*such thatx*∈Ω,〈(A-γf)x*-(I-B)Sx*,x-x*〉≥0,  ∀x∈Ω, whereΩis the set of the solutions of the following variational inequality:x*∈Ϝ,〈(A-S)x*,x-x*〉≥0,  ∀x∈Ϝ, whereA,Bare two strongly positive bounded linear operators,fis aρ-contraction,Sis a nonexpansive mapping, andϜis the fixed points set of a nonexpansive semigroup{T(s)}s≥0. We present a double-net convergence hierarchical to some elements inϜwhich solves the above hierarchical constrained variational inequalities.

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.

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