scholarly journals An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces

2011 ◽  
Vol 2011 (1) ◽  
pp. 748918 ◽  
Author(s):  
LC Zeng ◽  
Ching-Feng Wen ◽  
JC Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Fixed Point Approach ◽  
General Variational Inequalities ◽  
Hierarchical Fixed Point

scholarly journals Iterative algorithms of common solutions for a hierarchical fixed point problem, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yali Zhao ◽  
Xin Liu ◽  
Ruonan Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
System Of Variational Inequalities ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

AbstractIn this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature.

scholarly journals ON AN IMPLICIT HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES

2009 ◽  
Vol 80 (1) ◽  
pp. 117-124 ◽  
Author(s):  
FILOMENA CIANCIARUSO ◽  
VITTORIO COLAO ◽  
LUIGI MUGLIA ◽  
HONG-KUN XU
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Point Theory ◽  
Approximate Solutions ◽  
Fixed Point Problems ◽  
Viscosity Method ◽  
Norm Topology ◽  
Fixed Point Approach ◽  
Hierarchical Fixed Point ◽  
Hierarchical Fixed Point Problems

AbstractMoudafi and Maingé [Towards viscosity approximations of hierarchical fixed-point problems, Fixed Point Theory Appl. (2006), Art. ID 95453, 10pp] and Xu [Viscosity method for hierarchical fixed point approach to variational inequalities, Taiwanese J. Math.13(6) (2009)] studied an implicit viscosity method for approximating solutions of variational inequalities by solving hierarchical fixed point problems. The approximate solutions are a net (xs,t) of two parameters s,t∈(0,1), and under certain conditions, the iterated lim t→0lim s→0xs,t exists in the norm topology. Moudafi, Maingé and Xu stated the problem of convergence of (xs,t) as (s,t)→(0,0) jointly in the norm topology. In this paper we further study the behaviour of the net (xs,t); in particular, we give a negative answer to this problem.

Decay solutions for a class of fractional differential variational inequalities

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Tran Dinh Ke ◽  
Nguyen Van Loi ◽  
Valeri Obukhovskii
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fractional Derivatives ◽  
New Class ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Differential Variational Inequalities

AbstractOur aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

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