Coupled variational–hemivariational inequalities with constraints and history‐dependent operators

The aim of the paper is to study a new class of coupled variational–hemivariational inequalities with unilateral constraints and history‐dependent operators. First, by employing a fixed‐point theorem for history‐dependent operators combined with surjectivity theorem, we establish the existence and uniqueness of solution for coupled system. Second, we obtain a convergence result, namely, related penalized problems of solutions converge to the solution to the original system. Finally, we conclude with a new contact problem of the body pressure of two elastic materials.