scholarly journals k-Steps Explicit Iterative Algorithms to Solve Generalized System of Nonlinear Mixed Variational Inequalities

2021 ◽  
pp. 131-148
Author(s):  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Generalized System ◽  
Convergence Results ◽  
Generalized Systems ◽  
Mixed Variational Inequalities

The objective of this paper is to consider new generalized systems of nonlinear mixed variational inequalities including 3k-distinct nonlinear relaxed cocoercive operators. We proposed k-steps explicit iterative methods including projection operators for this considered system and present the equivalent fixed point problem of this new generalized systems of variational inequalities. This equivalent fixed point problem suggest to us k-steps explicit iterative algorithms to obtain an approximate solution of the considered system. Convergence results of k-step explicit iterative algorithms are obtained.

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 Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1189 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included.

scholarly journals Some Proximal Methods for Solving Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam Noor ◽  
Zhenyu Huang
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Methods ◽  
Proximal Point ◽  
Equivalent Formulation ◽  
New Methods ◽  
Special Cases ◽  
Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

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 Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1502
Author(s):  
Sun Young Cho
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Strict Pseudocontraction ◽  
Adaptive Step

In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality.

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.

Sign in / Sign up

Export Citation Format

Share Document