Error bounds for a class of history-dependent variational inequalities controlled by D-gap functions
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS(2023)
摘要
In the present paper, we are concerned with investigating error bounds for historydependent variational inequalities controlled by the difference gap (for brevity, D-gap) functions. First, we recall a class of elliptic variational inequalities involving the historydependent 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 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 D-gap function are derived under suitable conditions.
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关键词
. history-dependent operator,gap function,error bound,variational inequality
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