Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

2013 ◽  
Vol 159 (2) ◽  
pp. 399-411 ◽  
Author(s):  
Nguyen Buong ◽  
Nguyen Thi Hong Phuong
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Methods ◽  
Implicit Iteration

scholarly journals Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 424
Author(s):  
Lu-Chuan Ceng ◽  
Meijuan Shang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
General System ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings ◽  
Convex Feasibility ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Iteration Methods ◽  
Implicit Iteration

Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.

scholarly journals Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 218
Author(s):  
Lu-Chuan Ceng ◽  
Xiaoye Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Solution ◽  
Iteration Methods ◽  
Monotone Variational Inequality ◽  
Implicit Iteration

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

Explicit iteration methods for a class of variational inequalities in Banach spaces

2015 ◽  
Vol 59 (10) ◽  
pp. 16-22 ◽  
Author(s):  
Nguyen Buong ◽  
Nguyen Thi Hong Phuong ◽  
Nguyen Thi Thu Thuy
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Iteration Methods

Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

2017 ◽  
Vol 42 (2) ◽  
pp. 467-483
Author(s):  
Pham Thanh Hieu ◽  
Nguyen Thi Thu Thuy ◽  
Jean Jacques Strodiot
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Iteration Methods

scholarly journals Convergence theorems for composite viscosity approaches to systems variational inequalities in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6267-6281
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
General System ◽  
Inequality Constraint ◽  
Implicit And Explicit

In this paper, we study a general system of variational inequalities with a hierarchical variational inequality constraint for an infinite family of nonexpansive mappings. We introduce general implicit and explicit iterative algorithms. We prove the strong convergence of the sequences generated by the proposed iterative algorithms to a solution of the studied problems.

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