Exceptional family of elements for a generalized set-valued variational inequality in Banach spaces

Optimization ◽  
2011 ◽  
Vol 63 (2) ◽  
pp. 167-180 ◽  
Author(s):  
Zhong-Bao Wang ◽  
Nan-Jing Huang
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Exceptional Family Of Elements ◽  
Exceptional Family

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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