scholarly journals Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces

2011 ◽  
Vol 1 (2) ◽  
pp. 261-274 ◽  
Author(s):  
Ren-You Zhong ◽  
◽  
Nan-Jing Huang
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Mixed Variational Inequality ◽  
Strict Feasibility ◽  
Generalized Mixed Variational Inequality

scholarly journals On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen ◽  
Hui-Ying Hu ◽  
Long He ◽  
...  
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space. The relations between the Levitin–Polyak well-posedness and Hadamard well-posedness for a generalized mixed variational inequality are studied. The characterizations of Hadamard well-posedness for a generalized mixed variational inequality are established.

scholarly journals Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Inclusion Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

2018 ◽  
Vol 9 (3) ◽  
pp. 167-184 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Ferdinard Udochukwu Ogbuisi ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Monotone Operators ◽  
Convergence Result ◽  
Reflexive Banach Spaces ◽  
Strongly Monotone Operators ◽  
System Of Equilibrium Problems

Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

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