Algorithm method for solving the split general system of variational inequalities problem and fixed point problem of nonexpansive mapping with application

2018 ◽  
Vol 41 (17) ◽  
pp. 7766-7788 ◽  
Author(s):  
Keerati Siriyan ◽  
Atid Kangtunyakarn
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
System Of Variational Inequalities

scholarly journals Hybrid viscosity approximation methods for systems of variational inequalities and hierarchical fixed point problems

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1927-1947
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
System Of Variational Inequalities ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities with a hierarchical fixed point problem constraint for an infinite family of nonexpansive mappings. We show that the proposed algorithms converge strongly to a solution of the general system of variational inequalities, which is a unique solution of the hierarchical fixed point problem.

scholarly journals Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 187
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
General System ◽  
Inequality Constraint ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Common Fixed Point Problem ◽  
Monotone Variational Inequality

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

scholarly journals Systems of Variational Inequalities with Nonlinear Operators

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 338 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings ◽  
Common Fixed Point Problem

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.

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 Iterations for systems of variational inequalities, fixed points of pseudocontractions and zeros of accretive operators

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4769-4784
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
General System ◽  
Accretive Operator ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Accretive Operators ◽  
Common Solution ◽  
Pseudocontractive Mappings ◽  
Systems Of Variational Inequalities

In this paper, we introduce implicit composite three-step Mann iterations for finding a common solution of a general system of variational inequalities, a fixed point problem of a countable family of pseudocontractive mappings and a zero problem of an accretive operator in Banach spaces. Strong convergence of the suggested iterations are given.

scholarly journals Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yeong-Cheng Liou ◽  
Yonghong Yao ◽  
Chun-Wei Tseng ◽  
Hui-To Lin ◽  
Pei-Xia Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Nonlinear Operator ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Solution Set ◽  
Point Problem ◽  
General Variational Inequality

We consider a general variational inequality and fixed point problem, which is to find a pointx*with the property that (GVF):x*∈GVI(C,A)andg(x*)∈Fix(S)whereGVI(C,A)is the solution set of some variational inequalityFix(S)is the fixed points set of nonexpansive mappingS, andgis a nonlinear operator. Assume the solution setΩof (GVF) is nonempty. For solving (GVF), we suggest the following methodg(xn+1)=βg(xn)+(1-β)SPC[αnF(xn)+(1-αn)(g(xn)-λAxn)],n≥0. It is shown that the sequence{xn}converges strongly tox*∈Ωwhich is the unique solution of the variational inequality〈F(x*)-g(x*),g(x)-g(x*)〉≤0, for allx∈Ω.

scholarly journals Variational inequalities, variational inclusions and common fixed point problems in Banach spaces

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2939-2951
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Uniformly Smooth ◽  
Common Fixed Point Problem

In this paper, let X be a uniformly convex and q-uniformly smooth Banach space with 1 < q ? 2. We introduce and study modified implicit extragradient iterations for treating a common solution of a common fixed-point problem of a countable family of nonexpansive mappings, a general system of variational inequalities, and a variational inclusion in X.

Sign in / Sign up

Export Citation Format

Share Document