Error bounds for a class of history-dependent variational inequalities controlled by $\\mathcal{D}$-gap~functions

Authors : Boling Chen, Vo Minh Tam

Pages : 1550-1566

Doi:10.15672/hujms.1183739

View : 347 | Download : 399

Publication Date : 2023-11-03

Article Type : Research Paper

Abstract :In the present paper, we are concerned with investigating error bounds for history-dependent variational inequalities controlled by the difference gap (for brevity, $\\mathcal{D}$-gap) functions. First, we recall a class of elliptic variational inequalities involving the history-dependent operators (for brevity, HDVI). Then, we introduce a new concept of gap functions to the HDVI and propose the regularized gap function for the HDVI via the optimality condition for the concerning minimization problem. Consequently, the $\\mathcal{D}$-gap function for the HDVI depends on these regularized gap functions is established. Finally, error bounds for the HDVI controlled by the regularized gap function and the $\\mathcal{D}$-gap function are derived under suitable conditions.
Keywords : History dependent operator, Gap function, Error bound, Variational inequality