Abstract
In the present paper, we focus on a class of multivalued variational–hemivariational inequalities with pseudomonotone operator and constraint set in Hilbert spaces. By employing the penalty method and the Moreau–Yosida approximation technique, we construct an approximating problem for the original multivalued variational–hemivariational inequality under consideration. The main result in the paper shows that every weak cluster of the solution sequence for the approximating problem is always a solution of the original problem. Moreover, based on the obtained weak convergence result, another two strong convergence results are obtained when the condition of pseudomonotonicity is reinforced. Finally, we illustrate the application of our abstract results in the study of a frictionless contact problem in mechanics with unilateral constraint.
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