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

Author:

Hung Nguyen1,Qin Xiaolong2,Tam Vo3,Yao Jen-Chih4

Affiliation:

1. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam + Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

2. General Education Center, National Yunlin University of Science and Technology, Douliou, Taiwan

3. Department of Mathematics, Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

4. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, Taiwan

Abstract

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.

Publisher

National Library of Serbia

Subject

General Mathematics

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