scholarly journals GAP FUNCTIONS AND GLOBAL ERROR BOUNDS FOR SET-VALUED MIXED VARIATIONAL INEQUALITIES

2013 ◽  
Vol 17 (4) ◽  
pp. 1267-1286 ◽  
Author(s):  
Nan-jing Huang ◽  
Guo-ji Tang
Keyword(s):  
Variational Inequalities ◽  
Error Bounds ◽  
Global Error ◽  
Gap Functions ◽  
Mixed Variational Inequalities

scholarly journals Gap Functions and Error Bounds for Variational–Hemivariational Inequalities

2020 ◽  
Vol 169 (1) ◽  
pp. 691-709 ◽  
Author(s):  
Nguyen Van Hung ◽  
Stanislaw Migórski ◽  
Vo Minh Tam ◽  
Shengda Zeng
Keyword(s):  
Error Bounds ◽  
Global Error ◽  
Gap Functions ◽  
Hemivariational Inequalities ◽  
Elliptic Type ◽  
Generalized Gradient ◽  
Clarke Generalized Gradient ◽  
Regularized Gap Functions

Abstract In this paper we investigate the gap functions and regularized gap functions for a class of variational–hemivariational inequalities of elliptic type. First, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the variational–hemivariational inequalities. Then, the global error bounds for such inequalities in terms of regularized gap functions are derived by using the properties of the Clarke generalized gradient. Finally, an application to a stationary nonsmooth semipermeability problem is given to illustrate our main results.

scholarly journals Difference gap functions and global error bounds for random mixed equilibrium problems

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2739-2761
Author(s):  
Nguyen Hung ◽  
Xiaolong Qin ◽  
Vo Tam ◽  
Jen-Chih Yao
Keyword(s):  
Hilbert Spaces ◽  
Error Bounds ◽  
Equilibrium Problems ◽  
Gap Function ◽  
Global Error ◽  
Gap Functions ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Difference ◽  
Regularized Gap Functions

The aim of this paper is to study the difference gap (in short, D-gap) function and error bounds for a class of the random mixed equilibrium problems in real Hilbert spaces. Firstly, we consider regularized gap functions of the Fukushima type and Moreau-Yosida type. Then difference gap functions are established by using these terms of regularized gap functions. Finally, the global error bounds for random mixed equilibrium problems are also developed. The results obtained in this paper are new and extend some corresponding known results in literatures. Some examples are given for the illustration of our results.

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