Error bound analysis for split weak vector mixed quasi-variational inequality problems in fuzzy environment

Abstract

In this paper, we consider a new class of split weak vector mixed quasi-variational inequality problems in fuzzy environments (for short, SWQVIP). Our aim is to establish error bounds for the underlying problem SWQVIP via regularized gap functions. We first propose some regularized gap functions of the problem SWQVIP using the method of nonlinear scalarization functions. Then, error bounds for the problem SWQVIP are investigated based on regularized gap functions with some suitable conditions without monotonicity. Finally, some examples are given to illustrate our results. The main results obtained in this paper are new and extend some corresponding known results in the literature.

Keywords:

• Split weak vector mixed quasi-variational inequality problem
• regularized gap function
• fuzzy mapping
• error bound

2020 Mathematics Subject Classifications:

• 49J53
• 90C33
• 47S40
• 46S40

Acknowledgements

The authors are grateful to the editor and anonymous referees for their valuable remarks which improved the results and presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).