A hybrid iterative method with averaged mappings for hierarchical fixed point problems and variational inequalities

2015 ◽  
Vol 70 (3) ◽  
pp. 451-467 ◽  
Author(s):  
Bin Fan
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Fixed Point Problems ◽  
Hierarchical Fixed Point ◽  
Hybrid Iterative Method ◽  
Averaged Mappings ◽  
Hierarchical Fixed Point Problems

scholarly journals Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Preeyanuch Chuasuk ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Point Problems ◽  
Step Size ◽  
Inertial Method ◽  
Oligopolistic Market ◽  
Generalized Mixed Equilibrium ◽  
Hierarchical Fixed Point ◽  
Mixed Equilibrium ◽  
Hierarchical Fixed Point Problems

AbstractIn this paper, we present Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems for k-strictly pseudocontractive nonself-mappings. We establish that the weak convergence of the proposed accelerated iterative method with inertial terms involves a step size which does not require any prior knowledge of the operator norm under several suitable conditions in Hilbert spaces. Finally, the application to a Nash–Cournot oligopolistic market equilibrium model is discussed, and numerical examples are provided to demonstrate the effectiveness of our iterative method.

scholarly journals Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yaqin Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Viscosity Method ◽  
Hierarchical Fixed Point ◽  
The Common ◽  
Hierarchical Fixed Point Problems

A viscosity method for hierarchical fixed point problems is presented to solve variational inequalities, where the involved mappings are nonexpansive nonself-mappings. Solutions are sought in the set of the common fixed points of an infinite family of nonexpansive nonself-mappings. The results generalize and improve the recent results announced by many other authors.

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.

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